Domestication of Source Text in Literary Translation Prevails over Foreignization

Abstract

Domestication is a translation theory in which the source text (to be translated) is matched to the foreign reader by erasing its original linguistic and cultural difference. This match aims at making the target text (translated text) more fluent. On the contrary, foreignization is a translation theory in which the foreign reader is matched to the source text. This paper mathematically explores the degree of domestication/foreignization in current translation practice of texts written in alphabetical languages. A geometrical representation of texts, based on linear combinations of deep–language parameters, allows us (a) to calculate a domestication index which measures how much domestication is applied to the source text and (b) to distinguish language families. An expansion index measures the relative spread around mean values. This paper reports statistics and results on translations of (a) Greek New Testament books in Latin and in 35 modern languages, belonging to diverse language families; and (b) English novels in Western languages. English and French, although attributed to different language families, mathematically almost coincide. The requirement of making the target text more fluent makes domestication, with varying degrees, universally adopted, so that a blind comparison of the same linguistic parameters of a text and its translation hardly indicates that they refer to each other.

1. Introduction

Translation replaces a text in one language (source text) with an equivalent text in another language (target text). Most studies on translation report results not based on mathematical analysis of texts, as we do with a mathematical/statistical theory on alphabetical languages developed in a series of papers [1,2,3,4,5]. The mathematical approach adopted by scholars [6,7,8,9,10] considers neither Shannon’s communication theory [11] nor the fundamental relationship that linguistic parameters show with readers’ reading skills and short–term memory, included in our theory, which mathematically unifies the study of any alphabetical language.

Of all types of translation, literary translation is maybe the most demanding and difficult because the language of literature is different from ordinary or technical language and involves many challenges on the syntactic, lexical, semantic, and stylistic levels [12,13,14,15,16,17,18,19].

In studies on translation theory, especially of literary texts, scholars mention the concept of “equivalence” (or “sameness”) between the source text (to be translated) and the target text (translated) [20,21,22]. This concept, however, is loosely and poorly or never mathematically defined. On the contrary, our theory can mathematically “measure” how much texts differ from each other, with a multidimensional analysis [23].

Today, there is a consensus that the translator of literary texts is an active role player and the intermediary between the source text and the target text [14,24].

In relation to the translator’s role, however, two main theories of translation are discussed today: “domestication” and “foreignization” [24]. Domestication is a translation theory in which the translator tries to match the source text to the reader, mainly to the reader’s reading skills and the more general linguistic culture. Foreignization is a method in which the translator tries to match the reader to the source text, regardless of the reader’s reading skills and linguistic culture. In other words, domestication neglects the foreign reality, while foreignization retains the foreignness and cultural otherness of a foreign text.

In translation to English, for example, the dominant practice is domestication [24] because translation makes the target text more fluent. This is achieved, however, by erasing the linguistic and cultural difference of the foreign text; therefore, text fluency becomes the general criterion on which to judge a translation.

Our mathematical theory can measure the “equivalence” of source and target texts. In [23], for example, we showed how much J.R.R. Tolkien influenced the writings of C.S. Lewis, and in [25], we showed how much a recent English translation has modified the underlying mathematical structure of the most important Italian novel.

Out of the mathematical tools developed, to systematically study the domestication of source texts, we use a vector and geometrical representation of texts based on linear combinations of deep–language parameters [1,2,3]. From them, a probability of “error”, suitably defined, indicates how much a text can be confused with another text, quantified by an index giving the percentage of domestication [23,25]. In the present paper, we define another useful index, the “expansion” index, which measures the relative spread around mean values of the ensemble of vectors of two texts in their geometrical representation.

The theory is applied to a large set of the New Testament (NT) books originally written in Greek—namely the Gospels according to Matthew, Mark, Luke, John, the Book of Acts, the Epistle to the Romans, and the Apocalypse, for a total of 155 chapters, according to the traditional subdivision of the original Greek texts—and their translation to Latin and to 35 modern languages, texts partially studied also in [4].

The rationale for considering these NT books and their modern translations is based on its great importance for many scholars of multiple disciplines, and on the use of common language, not depending on any scientific/academic discipline. These translations strictly respect the subdivision in chapters and verses of the Greek texts—as they are fixed today, see [26] for recalling how interpunctions were introduced in the original scriptio continua texts—therefore, they can be studied at least at these two different levels (chapters and verses).

Notice that in this paper, “translation” is indistinguishable from “language” because we deal only with one translation per language. It is curious to notice, however, that in English and in Spanish, there are tens of different translations of the NT books [27].

For our analysis, as in References [2,4], we have chosen the chapter level because the amount of text is sufficiently large to assess reliable statistics on deep–language parameters. Therefore, for each translation/language, we have considered a data base of $155$ samples.

Our investigation shows that these Greek texts have been largely domesticated in modern translations. Moreover, to assess that domestication can also dominate translations in modern literature—not only the translation of ancient texts belonging to a diverse linguistic culture—we show, with few examples taken from English literature, that domestication prevails over foreignization, as in Italian literature [25].

Finally, notice that machine translation can use the tools developed in [1,2,3,4,5] and in the present paper to assess the quality of translation, at least mathematically and, therefore, objectively.

In synthesis, the new contribution of the present article shows that the requirement of making the target text of any language and epoch more fluent to the intended foreign reader makes domestication universally adopted—with varying degrees, mathematically measured—so that a blind comparison of the same linguistic parameters of a text and its translation hardly indicates that they refer to each other.

After this introductory section, in Section 2, we report on the data base of the Greek NT books, including their translations and statistics of totals of linguistic parameters; in Section 3, we define the deep–language parameters; in Section 4, we recall and discuss a geometrical representation of texts; in Section 5, we calculate the error probability and domestication index of texts; in Section 6, we explore the translation of the NT books from any language to any other language; in Section 7, we define and discuss the deep–language expansion factor; in Section 8, we study the domestication in translations of modern literature; and in Section 9, we summarize the main results and draw a conclusion.

2. Data Base and Statistics of Totals

In this section, we report on the statistics of totals regarding characters, words, sentences, and interpunctions (punctuation marks). We have calculated them from the digital texts (WinWord files) in the following manner: for each chapter, we have counted the number of characters, words, sentences, and interpunctions. Before doing so, however, we deleted the titles, footnotes, and other extraneous material present in the digital texts, as such information, for our analysis, can be considered “noise”.

The count is very simple, although time–consuming, and it does not require any understanding of the language considered or any specialized software. For each text block, WinWord directly provides the number of characters, words, and sentences. The number of sentences, however, was first calculated by replacing periods with periods (full stops): of course, this action does not change the text, but it gives the number of these substitutions and, therefore, the number of periods. The same procedure was performed for question marks and exclamation marks. The sum of the three totals gives the total number of sentences of the text block. The same procedure gives the total number of commas, colons, and semicolons. The sum of these latter values with the total number of sentences gives the total number of interpunctions.

Table 1. Language of translation and language family of the New Testament books (Matthew, Mark, Luke, John, Acts, Epistle to the Romans, and Apocalypse), with total number of characters ($C)$, words ($W)$, sentences ($S$), and interpunctions ($I$). The list concerning the genealogy of Jesus of Nazareth reported in Matthew 1.1–1.17 17 and in Luke 3.23–3.38 was deleted for not biasing the statistics of linguistic variables [2,4]. The source of the texts considered is reported in [2].

Language	Order	Abbreviation	Language Family	$\mathit{C}$	$\mathit{W}$	$\mathit{S}$	$\mathit{I}$
Greek	1	Gr	Hellenic	486,520	100,145	4759	13,698
Latin	2	Lt	Italic	467,025	90,799	5370	18,380
Esperanto	3	Es	Constructed	492,603	111,259	5483	22,552
French	4	Fr	Romance	557,764	133,050	7258	17,904
Italian	5	It	Romance	505,535	112,943	6396	18,284
Portuguese	6	Pt	Romance	486,005	109,468	7080	20,105
Romanian	7	Rm	Romance	513,876	118,744	7021	18,587
Spanish	8	Sp	Romance	505,610	117,537	6518	18,410
Danish	9	Dn	Germanic	541,675	131,021	8762	22,196
English	10	En	Germanic	519,043	122,641	6590	16,666
Finnish	11	Fn	Germanic	563,650	95,879	5893	19,725
German	12	Ge	Germanic	547,982	117,269	7069	20,233
Icelandic	13	Ic	Germanic	472,441	109,170	7193	19,577
Norwegian	14	Nr	Germanic	572,863	140,844	9302	18,370
Swedish	15	Sw	Germanic	501,352	118,833	7668	15,139
Bulgarian	16	Bg	Balto–Slavic	490,381	111,444	7727	20,093
Czech	17	Cz	Balto–Slavic	416,447	92,533	7514	19,465
Croatian	18	Cr	Balto–Slavic	425,905	97,336	6750	17,698
Polish	19	Pl	Balto–Slavic	506,663	99,592	8181	21,560
Russian	20	Rs	Balto–Slavic	431,913	92,736	5594	22,083
Serbian	21	Sr	Balto–Slavic	441,998	104,585	7532	18,251
Slovak	22	Sl	Balto–Slavic	465,280	100,151	8023	19,690
Ukrainian	23	Uk	Balto–Slavic	488,845	107,047	8043	22,761
Estonian	24	Et	Uralic	495,382	101,657	6310	19,029
Hungarian	25	Hn	Uralic	508,776	95,837	5971	22,970
Albanian	26	Al	Albanian	502,514	123,625	5807	19,352
Armenian	27	Ar	Armenian	472,196	100,604	6595	18,086
Welsh	28	Wl	Celtic	527,008	130,698	5676	22,585
Basque	29	Bs	Isolate	588,762	94,898	5591	19,312
Hebrew	30	Hb	Semitic	372,031	88,478	7597	15,806
Cebuano	31	Cb	Austronesian	681,407	146,481	9221	16,788
Tagalog	32	Tg	Austronesian	618,714	128,209	7944	16,405
Chichewa	33	Ch	Niger–Congo	575,454	94,817	7560	15,817
Luganda	34	Lg	Niger–Congo	570,738	91,819	7073	16,401
Somali	35	Sm	Afro–Asiatic	584,135	109,686	6127	17,765
Haitian	36	Ht	French Creole	514,579	152,823	10,429	23,813
Nahuatl	37	Nh	Uto–Aztecan	816,108	121,600	9263	19,271

lists languages of translation and language family of the New Testament books considered, together with the total number of characters, words, sentences, and interpunctions. Appendix A reports the list of mathematical symbols, along with their meanings.

Figure 1 and Figure 2 show the histograms of the values of Table 1, fitted with a log–normal probability density model, whose mean and standard deviation were calculated from the linear mean and standard deviation values (see Appendix B).

We defined the relative normalized difference between the linguistic quantity in Greek ($g)$ and that in translation ($t)$ of the parameters reported in Table 1:

$$\eta =100\times {\displaystyle \frac{t-g}{g}}$$

(1)

Table 2. Mean and standard deviation of the normalized difference, $\eta$ (%), in Equation (1), for the indicated linguistic parameter.

	Characters	Words	Sentences	Interpunctions
Mean	6.82	11.09	49.30	39.07
Standard deviation	15.99	2.14	26.71	17.43

shows the mean and standard deviation of $\eta$. Figure 1 and Figure 2 and the synthetic statistics reported in Table 2 do show that translation of the Greek texts is not at all verbatim, and it is quite different from language to language. All mean values are greater than the Greek value, with very large differences, especially in sentences and interpunctions. In the next section, we deepen the study of these differences.

3. Deep–Language Parameters

We recall the so–called surface deep–language parameters [1,2]. These parameters are not consciously managed by a writer; therefore, they are useful to assess “equivalence” or “sameness” of texts beyond writer’s awareness. To avoid possible misunderstanding, these variables refer to the “surface” structure of texts (i.e., what we read or write), not to the “deep” structure mentioned in cognitive theory. How the human brain analyzes the parts of a sentence (parsing) and describes their syntactic roles is still a major question in cognitive neuroscience [28,29,30,31].

Let $n_C$, $n_W$, $n_I$, and $n_{I_P}$ be the number of characters, words, interpunctions, and word intervals per chapter, respectively:

Number of characters per word, $C_P$:

$${\mathit{C}}_{\mathit{P}}={\displaystyle \frac{{\mathit{n}}_{\mathit{C}}}{{\mathit{n}}_{\mathit{W}}}}$$

(2)

Number of words per sentence, $P_F$:

$${\mathit{P}}_{\mathit{F}}={\displaystyle \frac{{\mathit{n}}_{\mathit{W}}}{{\mathit{n}}_{\mathit{S}}}}$$

(3)

Number of interpunctions per word, referred to as the word interval, $I_P$:

$${\mathit{I}}_{\mathit{P}}={\displaystyle \frac{{\mathit{n}}_{\mathit{I}}}{{\mathit{n}}_{\mathit{W}}}}$$

(4)

Number of word intervals per sentence, $M_F$:

$${\mathit{M}}_{\mathit{F}}={\displaystyle \frac{{\mathit{n}}_{{\mathit{I}}_{\mathit{P}}}}{{\mathit{n}}_{\mathit{S}}}}$$

(5)

Table 3. Mean value (left number of column, $<>$) and standard deviation (right number, $s$) of the surface deep–language parameters in the indicated language of the New Testament books (Matthew, Mark, Luke, John, Acts, Epistle to the Romans, and Apocalypse), calculated from 155 samples in each language. For example, in Greek, $<P_F> =23.07$, with a standard deviation $6.65$.

Language	${\mathit{P}}_{\mathit{F}}$	${\mathit{I}}_{\mathit{P}}$	${\mathit{C}}_{\mathit{P}}$	${\mathit{M}}_{\mathit{F}}$
	$\mathbf{<}{\mathit{P}}_{\mathit{F}}\mathbf{>}\hspace{1em}\mathit{s}$	$\mathbf{<}{\mathit{I}}_{\mathit{P}}\mathbf{>}\hspace{1em}\mathit{s}$	$\mathbf{<}{\mathit{C}}_{\mathit{P}}\mathbf{>}\hspace{1em}\mathit{s}$	$\mathbf{<}{\mathit{M}}_{\mathit{F}}\mathbf{>}\hspace{1em}\mathit{s}$
Greek	23.07  6.65	7.47  1.09	4.86  0.25	3.08  0.73
Latin	18.28  4.77	5.07  0.68	5.16  0.28	3.60  0.77
Esperanto	21.83  5.22	5.05  0.57	4.43  0.20	4.30  0.76
French	18.73  2.51	7.54  0.85	4.20  0.16	2.50  0.32
Italian	18.33  3.27	6.38  0.95	4.48  0.19	2.89  0.40
Portuguese	16.18  3.25	5.54  0.59	4.43  0.20	2.93  0.56
Romanian	18.00  4.19	6.49  0.74	4.34  0.19	2.78  0.65
Spanish	19.07  3.79	6.55  0.82	4.30  0.19	2.91  0.47
Danish	15.38  2.15	5.97  0.64	4.14  0.16	2.59  0.33
English	19.32  3.20	7.51  0.93	4.24  0.17	2.58  0.39
Finnish	17.44  4.09	4.94  0.56	5.90  0.31	3.54  0.75
German	17.23  2.77	5.89  0.60	4.68  0.19	2.94  0.45
Icelandic	15.72  2.58	5.69  0.67	4.34  0.18	2.77  0.39
Norwegian	15.21  1.43	7.75  0.84	4.08  0.13	1.98  0.22
Swedish	15.95  2.17	8.06  1.35	4.23  0.18	2.01  0.31
Bulgarian	14.97  2.61	5.64  0.64	4.41  0.19	2.67  0.43
Czech	13.20  3.10	4.89  0.65	4.51  0.21	2.71  0.61
Croatian	15.32  3.54	5.62  0.75	4.39  0.22	2.72  0.49
Polish	12.34  1.93	4.65  0.43	5.10  0.22	2.67  0.40
Russian	17.90  4.46	4.28  0.46	4.67  0.27	4.18  0.92
Serbian	14.46  2.42	5.81  0.69	4.24  0.20	2.50  0.39
Slovak	12.95  2.10	5.18  0.61	4.65  0.23	2.51  0.36
Ukrainian	13.81  2.18	4.72  0.41	4.56  0.26	2.95  0.58
Estonian	17.09  3.89	5.45  0.66	4.89  0.24	3.14  0.64
Hungarian	17.37  4.54	4.25  0.45	5.31  0.29	4.09  0.93
Albanian	22.72  4.86	6.52  0.78	4.07  0.22	3.48  0.61
Armenian	16.09  3.07	5.63  0.52	4.75  0.40	2.86  0.47
Welsh	24.27  4.75	5.84  0.44	4.04  0.15	4.16  0.76
Basque	18.09  4.31	4.99  0.52	6.22  0.27	3.63  0.81
Hebrew	12.17  2.04	5.65  0.59	4.22  0.17	2.16  0.33
Cebuano	16.15  1.71	8.82  1.01	4.65  0.10	1.85  0.22
Tagalog	16.98  3.24	7.92  0.82	4.83  0.17	2.16  0.44
Chichewa	12.89  1.79	6.18  0.87	6.08  0.18	2.10  0.25
Luganda	13.65  2.78	5.74  0.82	6.23  0.23	2.39  0.40
Somali	19.57  5.50	6.37  1.01	5.32  0.16	3.06  0.65
Haitian	14.87  1.83	6.55  0.71	3.37  0.10	2.28  0.26
Nahuatl	13.36  1.70	6.47  0.91	6.71  0.24	2.08  0.24

reports the mean and standard deviation of these parameters in the indicated translation. Notice that the values of these parameters, if calculated from the totals of Table 1, are always less or equal to those reported in Table 3 (see the proof in [25]). For example, in Greek, $<P_F> =23.07$, while the value calculated from Table 1 is $\mathrm{100,145}/4759=21.04<23.07$, as theoretically expected.

Table 3 shows a large spread compared to the original Greek values. These differences will largely affect the geometrical representation, the probability of error, the domestication index, and the expansion factor, all issues discussed in the next sections.

4. Geometrical Representation of Texts

The mean values reported in Table 3 can be used to model texts as vectors in the first quadrant of a Cartesian orthogonal coordinates plane; a representation is discussed in detail in [1,2,3], and here, it is briefly recalled for the reader’s benefit. This geometrical representation of texts allows us to calculate the probability that a text/author can be confused with another one [26,28]. The conditional probability and the domestication index can indicate a probable influence of a text on another, as shown in [26,28]. In our case, it indicates how much a translation differs from or is similar to the original text.

Let us consider the following six vectors of the indicated components of deep–language variables: $\overrightarrow{R_1}=({<C}_P>,{<P}_F>$), $\overrightarrow{R_2}=({<M}_F>,{<P}_F>$), $\overrightarrow{R_3}=(<I_P>,<P_F>$), $\overrightarrow{R_4}=({<C}_P>,{<M}_F>$), $\overrightarrow{R_5}=({<I}_P>,{<M}_F>$), $\overrightarrow{R_6}=({<I}_P>,<C_P>$) and their resulting vector sum:

$$\overrightarrow{R}={\sum }_{k=1}^6\overrightarrow{R_k}=x\overrightarrow{i}+y\overrightarrow{j}$$

(6)

Notice that deciding which parameter is reported in abscissa or in ordinate is not fundamental because, once the choice is made, the numerical results will depend on it, but not comparisons and conclusions. Texts are mathematically more connected as the distance between the ending points of vector Equation (6) decreases.

By considering the vector components $x$ and $y$ of Equation (6), we obtain the scatterplots shown in Figure 3, where $X$ and $Y$ are normalized coordinates calculated by setting Haitian at the origin $(X=0, Y=0)$ and Greek at $(X=1, Y=1)$, according to the linear transformation:

$$X={\displaystyle \frac{x-x_{Haitian}}{{x_{Greek}-x}_{Haitian}}}$$

(7)

$$Y={\displaystyle \frac{y-y_{Haitian}}{{y_{Greek}-y}_{Haitian}}}$$

(8)

From the scatterplot shown in Figure 3, we can observe the following facts.

Latin, Italian, Spanish, French, and Romanian are very close to each other, very likely because they all belong to the same Romance family (languages mostly derived from Latin), with the exception of Portuguese.

Greek is largely displayed from all other languages, therefore confirming the large differences of the Greek totals compared to those of the other languages (Table 2).

Bulgarian, Czech, Croatian, Polish, Serbian, Slovak, and Ukrainian are close to each other, very likely because they all belong to the same Balto–Slavic family.

Chichewa and Luganda are close to each other, both belonging to the Niger–Congo family; Cebuano and Tagalog are also very close to each other, both belonging to the Austronesian family.

English and French, although attributed to different families, almost coincide, at least in the translations considered here (both from the Vatican website; see [2]). This coincidence, and also the small distance between English and all other Romance languages, can be partially explained by the fact that many English words—English contains up to 65% of Latinisms, i.e., words of Latin and Old French origin—and several sentence structure come French and/or from Latin, a language from which Romance languages derive.

In conclusion, the geometrical representation based on the means of the deep–language parameters allows us to distinguish language family and relative distances.

Now, a more refined analysis can indicate whether a text may be confused with another belonging to the same or diverse language family. The standard deviation of the four deep–language variables (Table 3) does introduce vectors scattering; therefore, a text/translation can extend itself in an area around the ending point of the vector Equation (6). In other words, a text can “overlap” with other texts and can be, therefore, mathematically confused with another one. This fact can be measured by an “error” probability and a domestication index [26,28], which depend on the relative distance between mean vectors and standard deviations, as discussed in the next section.

5. Error Probability and Domestication Index

Besides the mean vector, $\overrightarrow{R}$, given by Equation (6), we can consider a further vector, $\overrightarrow{\rho }$, due to the standard deviation of the four deep–language variables, adding up to $\overrightarrow{R}$ [26]. In this case, the final vector modelling a text/translation is given by the following:

$$\overrightarrow{T}=\overrightarrow{R}+\overrightarrow{\rho }$$

(9)

Now, to gain some insight into this description, we consider the area of a circle centered at the ending point of $\overrightarrow{R}$. The radius, $\rho ,$ is calculated as follows [23]. First, we add the variances of the deep–language variables that determine the components $x$ and $y$ of $\overrightarrow{R}$—let the total sums be ${\sigma }_x^2$, ${\sigma }_y^2$—and then we calculate the average value, ${\sigma }_{\rho }^2=0.5\times ({\sigma }_x^2+{\sigma }_y^2)$, and finally, we set the following:

$$\rho ={\sigma }_{\rho }$$

(10)

Because in calculating the coordinates $x$ and $y$ of $\overrightarrow{R}$, a deep–language variable can be summed twice or more in Equation (6), we add its standard deviation (Table 3) two or more times before squaring and coordinates normalization, as shown in [23].

Now, we can estimate the (conditional) probability that a text is confused with another by calculating ratios of overlapping areas. This procedure is correct if we assume that the bivariate density function of the normalized coordinates, ${\rho }_X \mathrm{a}\mathrm{n}\mathrm{d} {\rho }_Y$, centred at $\overrightarrow{R}$, is uniform [32,33,34].

As discussed in [23], the hypothesis of substantial uniformity around $\overrightarrow{R}$ should hold at least within 1–sigma bounds, by noting that the coordinates $X, Y$ are likely distributed according to a Gaussian bivariate density. Now, the four deep–language variables, which are combined in Equation (6) linearly, can be modelled as log–normal [1]; therefore, for the central–limit theorem [32], we should expect approximately a Gaussian model of the coordinates $X, Y$, but with a significantly larger standard deviation than that of the single deep–language variables. Therefore, in the area close to $\overrightarrow{R}$, the bivariate density function should not be very peaked, hence the uniform density modelling, at least within 1–sigma bounds.

Now, we can calculate the following probabilities. Let $A$ be the common area of two 1–sigma circles (i.e., the area proportional to the joint probability of two texts), let $A_1$ be the area of 1–sigma circle of text 1, and let $A_2$ the area of 1–sigma circle of text 2. Now, since probabilities are proportional to areas, we get the following relationships:

$${\displaystyle \frac{A}{A_1}}={\displaystyle \frac{P(A_1,A_2)}{P\left(A_1\right)}}={\displaystyle \frac{P(A_2/A_1)P\left(A_1\right)}{P\left(A_1\right)}}=P(A_2/A_1)$$

(11)

$${\displaystyle \frac{A}{A_2}}={\displaystyle \frac{P(A_1,A_2)}{P\left(A_2\right)}}={\displaystyle \frac{P(A_1/A_2)P\left(A_2\right)}{P\left(A_2\right)}}=P(A_1/A_2)$$

(12)

Therefore, $A/A_1$ gives the conditional probability $P(A_2/A_1)$ that part of text 2 can be confused with text 1; $A/A_2$ gives the conditional probability $P(A_1/A_2)$ that part of text 1 can be confused with text 2. $P(A_2/A_1)=1$ means $A=A_1$; therefore, text 1 can be fully confused with text 2. And $P(A_1/A_2)=1$ means ${A=A}_2$; therefore, text 2 can be fully confused with text 1.

We recall a synthetic parameter which highlights how much two texts can be confused with each other. The parameter is the average conditional probability of error:

$$p_e=P(A_2/A_1)P\left(A_1\right)+P(A_1/A_2)P\left(A_2\right)$$

(13)

Now, since, in comparing two texts, we can assume $P\left(A_1\right)=P\left(A_2\right)=0.5$, we get the following:

$$p_e=0.5\times \left[P\right(A_2/A_1)+P(A_1/A_2\left)\right]$$

(14)

If $p_e=0$, there is no intersection between the two 1–sigma circles, and the two texts cannot be confused with each other; therefore, there is no mathematical connection (at least at 1–sigma) involving the deep–language parameters. If $p_e=1$, the two texts can be totally confused; the two 1–sigma circles coincide.

From the conditional probability, we get the domestication index, $D$ [25], given by the following:

$$D=1-p_e$$

(15)

with the following meaning: if $D=1$, then $p_e=0$, and domestication is total; if $D=0$, then $p_e=1$, and foreignization is total.

Figure 4, Figure 5 and Figure 6 show 1–sigma circles centered at mean vectors. From these figures, we can calculate the error probability and the domestication index of the translations from Greek, but also the domestication index in conjectural translations from any language to any other language, as discussed in the next section.

Table A2. Domestication index, $D$ (%). Red numbers refer to languages with $D<30$. The last two rows give the following data: number of languages with $D<100$, mean and standard deviation of $D$ considering only cases $D<100$; mean and standard deviation of the expansion factor, $E$. For example, in Greek, 19 languages show $D=100\%$; mean $=75.19\%$, with standard deviation 26.23%. The mean expansion factor is $m_E=0.564$, with standard deviation of $s_E=0.136$.

	Gr	Lt	Es	Fr	It	Pt	Rm	Sp	Dn	En	Fn	Ge	Ic
Gr	0	80.72	75.80	71.83	84.13	100	88.43	79.40	100	62.55	80.04	99.70	100
Lt	80.72	0	66.76	25.32	10.93	59.10	11.68	16.11	77.55	31.02	43.44	28.28	68.36
Es	75.80	66.76	0	76.99	68.78	97.20	70.48	56.64	100	69.42	94.98	88.90	100
Fr	71.83	25.32	76.99	0	28.93	90.16	37.18	31.63	100	14.90	37.09	55.60	97.68
It	84.13	10.93	68.78	28.93	0	62.40	9.82	15.24	82.49	35.40	49.35	27.05	72.66
Pt	100	59.10	97.20	90.16	62.40	0	51.32	70.42	24.26	91.86	90.10	49.43	13.21
Rm	88.43	11.68	70.48	37.18	9.82	51.32	0	21.01	71.09	43.73	52.90	24.53	61.37
Sp	79.40	16.11	56.64	31.63	15.24	70.42	21.01	0	89.97	33.11	58.43	40.18	80.82
Dn	100	77.55	100	100	82.49	24.26	71.09	89.97	0	100	100	73.78	12.90
En	62.55	31.02	69.42	14.90	35.40	91.86	43.73	33.11	100	0	42.69	61.33	98.51
Fn	80.04	43.44	94.98	37.09	49.35	90.10	52.90	58.43	100	42.69	0	59.87	95.96
Ge	99.70	28.28	88.90	55.60	27.05	49.43	24.53	40.18	73.78	61.33	59.87	0	61.39
Ic	100	68.36	100	97.68	72.66	13.21	61.37	80.82	12.90	98.51	95.96	61.39	0
Nr	100	58.73	100	81.56	65.72	70.66	59.48	79.77	83.55	85.61	58.90	57.03	75.18
Sw	91.25	49.09	98.02	52.43	53.43	75.45	53.18	64.71	87.00	59.37	26.03	50.32	80.09
Bg	100	78.88	100	100	83.51	31.22	73.27	91.25	14.76	100	99.01	73.66	20.30
Cz	100	100	100	100	100	75.90	99.67	100	62.35	100	100	100	68.96
Cr	100	70.26	100	95.40	73.45	20.82	63.91	81.08	24.51	96.74	92.70	60.70	18.15
Pl	100	100	100	100	100	96.23	100	100	90.63	100	100	100	92.29
Rs	100	51.65	69.17	79.31	52.35	42.75	44.67	51.54	59.32	79.64	90.01	52.72	52.17
Sr	100	88.91	100	100	93.00	45.44	84.35	98.32	26.72	100	100	86.32	35.29
Sl	100	100	100	100	100	81.86	100	100	70.97	100	100	100	75.41
Uk	100	100	100	100	100	72.12	100	100	57.55	100	100	100	64.60
Et	96.84	26.17	84.58	51.96	26.98	40.83	18.61	40.04	60.11	58.82	56.17	20.11	50.13
Hn	93.76	20.87	76.08	47.27	20.26	41.17	10.59	30.99	60.69	53.67	57.80	23.81	51.06
Al	60.03	72.20	24.17	76.68	75.12	100	78.34	63.60	100	66.60	94.36	96.05	100
Ar	100	47.77	99.07	78.66	51.77	30.68	41.63	64.38	47.65	82.59	73.48	32.40	37.05
Wl	74.49	95.99	42.21	100	98.50	100	99.23	91.42	100	95.06	100	100	100
Bs	68.06	63.02	98.57	52.36	69.46	100	73.72	74.17	100	50.73	29.90	84.97	100
Hb	100	100	100	100	100	97.84	100	100	91.60	100	100	100	94.38
Cb	91.97	91.19	100	91.41	96.75	100	97.63	99.82	100	89.26	59.92	100	100
Tg	82.08	71.64	100	67.57	78.57	100	81.00	85.02	100	67.18	33.83	90.31	100
Ch	100	100	100	100	100	100	100	100	100	100	96.07	100	100
Lg	100	99.19	100	100	100	100	100	100	100	100	83.49	100	100
Sm	47.46	48.84	76.53	33.38	52.25	94.68	58.63	52.30	100	28.27	35.49	68.36	99.39
Ht	100	99.14	100	100	100	62.07	96.14	100	50.99	100	100	99.90	57.00
Nh	100	100	100	100	100	100	100	100	100	100	100	100	100
$D$	19	30	20	24	28	28	30	28	23	25	27	27	27
	75.19	55.09	71.72	57.30	54.94	59.97	55.92	59.33	57.41	59.92	62.67	58.03	60.53
	22.01	28.16	24.95	26.67	28.13	27.53	28.89	27.32	27.16	26.21	26.23	26.65	28.76
$E$	0.564	0.801	0.774	1.079	0.906	1.100	0.867	0.898	1.351	0.927	0.931	1.215	1.208
	0.136	0.193	0.187	0.260	0.219	0.265	0.209	0.217	0.326	0.223	0.225	0.293	0.291

,

Table A3. Domestication index (see Table A2 for more details).

	Nr	Sw	Bg	Cz	Cr	Pl	Rs	Sr	Sl	Uk	Et	Hn
Gr	100	91.25	100	100	100	100	100	100	100	100	96.84	93.76
Lt	58.73	49.09	78.88	100	70.26	100	51.65	88.91	100	100	26.17	20.87
Es	100	98.02	100	100	100	100	69.17	100	100	100	84.58	76.08
Fr	81.56	52.43	100	100	95.40	100	79.31	100	100	100	51.96	47.27
It	65.72	53.43	83.51	100	73.45	100	52.35	93.00	100	100	26.98	20.26
Pt	70.66	75.45	31.22	75.90	20.82	96.23	42.75	45.44	81.86	72.12	40.83	41.17
Rm	59.48	53.18	73.27	99.67	63.91	100	44.67	84.35	100	100	18.61	10.59
Sp	79.77	64.71	91.25	100	81.08	100	51.54	98.32	100	100	40.04	30.99
Dn	83.55	87.00	14.76	62.35	24.51	90.63	59.32	26.72	70.97	57.55	60.11	60.69
En	85.61	59.37	100	100	96.74	100	79.64	100	100	100	58.82	53.67
Fn	58.90	26.03	99.01	100	92.70	100	90.01	100	100	100	56.17	57.80
Ge	57.03	50.32	73.66	100	60.70	100	52.72	86.32	100	100	20.11	23.81
Ic	75.18	80.09	20.30	68.96	18.15	92.29	52.17	35.29	75.41	64.60	50.13	51.06
Nr	0	31.35	75.66	99.76	67.21	100	88.58	85.47	99.13	100	46.52	54.63
Sw	31.35	0	82.53	100	77.00	100	84.94	90.44	99.98	100	47.93	53.51
Bg	75.66	82.53	0	55.26	18.90	76.50	67.31	17.49	58.09	49.79	61.27	63.54
Cz	99.76	100	55.26	0	54.58	44.80	93.78	40.07	25.91	25.21	95.31	95.92
Cr	67.21	77.00	18.90	54.58	0	72.17	56.35	22.77	56.52	45.52	52.49	54.66
Pl	100	100	76.50	44.80	72.17	0	100	64.60	26.91	69.24	100	100
Rs	88.58	84.94	67.31	93.78	56.35	100	0	76.26	99.82	93.11	48.85	40.74
Sr	85.47	90.44	17.49	40.07	22.77	64.60	76.26	0	43.58	32.35	74.05	75.72
Sl	99.13	99.98	58.09	25.91	56.52	26.91	99.82	43.58	0	39.74	97.38	98.56
Uk	100	100	49.79	25.21	45.52	69.24	93.11	32.35	39.74	0	96.69	96.88
Et	46.52	47.93	61.27	95.31	52.49	100	48.85	74.05	97.38	96.69	0	10.82
Hn	54.63	53.51	63.54	95.92	54.66	100	40.74	75.72	98.56	96.88	10.82	0
Al	100	98.86	100	100	100	100	84.88	100	100	100	91.79	84.71
Ar	44.57	54.29	45.79	88.24	37.02	99.03	57.92	60.88	89.83	89.87	25.21	32.08
Wl	100	100	100	100	100	100	99.61	100	100	100	100	100
Bs	84.12	47.34	100	100	100	100	99.98	100	100	100	79.51	79.26
Hb	100	100	82.16	28.29	77.78	44.54	100	68.08	34.63	53.88	100	100
Cb	95.50	57.21	100	100	100	100	100	100	100	100	98.70	99.23
Tg	80.68	40.56	100	100	100	100	100	100	100	100	83.70	84.81
Ch	96.35	74.62	100	100	100	100	100	100	100	100	100	100
Lg	84.79	60.90	100	100	100	100	100	100	100	100	99.52	100
Sm	79.27	54.49	100	100	97.80	100	87.96	100	100	100	67.55	65.68
Ht	100	100	53.58	47.67	44.93	94.58	75.31	45.11	72.02	40.50	91.49	89.83
Nh	100	97.79	100	100	100	100	100	100	100	100	100	100
$D$	28	31	24	18	27	13	29	23	18	16	32	31
	71.06	64.33	57.24	61.21	56.79	67.04	68.30	58.92	65.02	57.94	59.38	57.05
	21.83	23.46	26.69	29.58	26.32	29.17	22.81	27.50	30.01	26.93	28.73	28.51
$E$	1.264	0.796	1.223	1.091	0.964	1.684	0.892	1.224	1.385	1.550	0.939	0.879
	0.305	0.192	0.295	0.263	0.233	0.406	0.215	0.295	0.334	0.374	0.227	0.212

and

Table A4. Domestication index (see Table A2 for more details).

	Al	Ar	Wl	Bs	Hb	Cb	Tg	Ch	Lg	Sm	Ht	Nh
Gr	60.03	100	74.49	68.06	100	91.97	82.08	100	100	47.46	100	100
Lt	72.20	47.77	95.99	63.02	100	91.19	71.64	100	99.19	48.84	99.14	100
Es	24.17	99.07	42.21	98.57	100	100	100	100	100	76.53	100	100
Fr	76.68	78.66	100	52.36	100	91.41	67.57	100	100	33.38	100	100
It	75.12	51.77	98.50	69.46	100	96.75	78.57	100	100	52.25	100	100
Pt	100	30.68	100	100	97.84	100	100	100	100	94.68	62.07	100
Rm	78.34	41.63	99.23	73.72	100	97.63	81.00	100	100	58.63	96.14	100
Sp	63.60	64.38	91.42	74.17	100	99.82	85.02	100	100	52.30	100	100
Dn	100	47.65	100	100	91.60	100	100	100	100	100	50.99	100
En	66.60	82.59	95.06	50.73	100	89.26	67.18	100	100	28.27	100	100
Fn	94.36	73.48	100	29.90	100	59.92	33.83	96.07	83.49	35.49	100	100
Ge	96.05	32.40	100	84.97	100	100	90.31	100	100	68.36	99.90	100
Ic	100	37.05	100	100	94.38	100	100	100	100	99.39	57.00	100
Nr	100	44.57	100	84.12	100	95.50	80.68	96.35	84.79	79.27	100	100
Sw	98.86	54.29	100	47.34	100	57.21	40.56	74.62	60.90	54.49	100	97.79
Bg	100	45.79	100	100	82.16	100	100	100	100	100	53.58	100
Cz	100	88.24	100	100	28.29	100	100	100	100	100	47.67	100
Cr	100	37.02	100	100	77.78	100	100	100	100	97.80	44.93	100
Pl	100	99.03	100	100	44.54	100	100	100	100	100	94.58	100
Rs	84.88	57.92	99.61	99.98	100	100	100	100	100	87.96	75.31	100
Sr	100	60.88	100	100	68.08	100	100	100	100	100	45.11	100
Sl	100	89.83	100	100	34.63	100	100	100	100	100	72.02	100
Uk	100	89.87	100	100	53.88	100	100	100	100	100	40.50	100
Et	91.79	25.21	100	79.51	100	98.70	83.70	100	99.52	67.55	91.49	100
Hn	84.71	32.08	100	79.26	100	99.23	84.81	100	100	65.68	89.83	100
Al	0	100	32.78	95.68	100	100	100	100	100	69.43	100	100
Ar	100	0	100	94.89	100	100	96.29	100	100	84.61	86.88	100
Wl	32.78	100	0	100	100	100	100	100	100	92.47	100	100
Bs	95.68	94.89	100	0	100	45.11	21.71	98.42	87.34	26.36	100	100
Hb	100	100	100	100	0	100	100	100	100	100	81.40	100
Cb	100	100	100	45.11	100	0	28.65	82.64	67.25	58.69	100	81.32
Tg	100	96.29	100	21.71	100	28.65	0	89.06	73.98	41.17	100	95.74
Ch	100	100	100	98.42	100	82.64	89.06	0	18.68	99.98	100	69.22
Lg	100	100	100	87.34	100	67.25	73.98	18.68	0	92.36	100	68.32
Sm	69.43	84.61	92.47	26.36	100	58.69	41.17	99.98	92.36	0	100	100
Ht	100	86.88	100	100	81.40	100	100	100	100	100	0	100
Nh	100	100	100	100	100	81.32	95.74	69.22	68.32	100	100	0
$D$	18	29	11	23	12	19	21	10	12	27	19	6
	70.29	61.19	74.71	66.29	62.88	75.38	66.36	72.50	69.65	63.46	67.82	68.73
	26.20	26.24	32.54	27.21	29.40	26.98	26.65	33.31	29.67	25.59	25.77	32.80
$E$	0.773	1.161	0.866	0.907	1.441	1.057	0.980	1.173	1.049	0.659	1.356	1.139
	0.186	0.280	0.209	0.219	0.348	0.254	0.236	0.283	0.253	0.159	0.327	0.275

in Appendix C reports the values of $D(\%)$ for all languages.

From Figure 4, Figure 5 and Figure 6, we can see the following interesting features.

Figure 4a: The mean vectors of Latin and Romance languages, except Portuguese, not only practically coincide, but they also show similar 1–sigma radii; therefore, these translations spread in the same way. This is a robust result that locates and can distinguish Romance languages from other families. For this language family, $<\rho > =0.37$.

Figure 4b: Germanic languages are quite scattered; they do not show the closeness of Romance languages. Curiously, English and French coincide not only according to mean vectors but also to similar spread, as Figure 6b shows. For this language family, $<\rho > =0.34$.

Figure 5a: The mean vectors of Balto–Slavic languages are close to each other, and they also show similar 1–sigma radii, a robust result that locates this language family. For this language family, $<\rho > =0.29$.

Figure 5b: The languages reported belong to different families, and this fact can be noticed both in distance between mean vectors and diverse spread.

Figure 6a: Chichewa and Luganda, both belonging to the Niger–Congo family, are very close to each other, and they show similar 1–sigma radii; the same can be said for Cebuano and Tagalog, both belonging to the Austronesian family.

In conclusion, Figure 4, Figure 5 and Figure 6 confirm the distinction of language families according to mean vectors, and they indicate that, within a family, the spread is similar.

Now, we can calculate the domestication index. Figure 7 shows $D$ (%) versus translation language, with language order number according to Table 1. Notice that, in 18 translations, $D=100\%$, and hence $p_e=0$; therefore, circles do not overlap. The smallest $D=47.46\%$ is given by the Somali translation (language order 35).

Table A2, Table A3 and Table A4 (first column) in Appendix C lists the values drawn in Figure 7. From Figure 7, we can conclude that the degree of domestication of the Greek texts is very high, mostly greater than 50%. In other words, these translations are very far from being verbatim, a conclusion reached for Matthew only by considering information theory parameters [2,4,5,6].

Finally, Figure 8 shows the scatterplot between $D$ and mean vectors distance, $d$, from Greek, given by the following:

$$d=\sqrt{{(X-X_{Gr})}^2+{(Y-Y_{Gr})}^2}$$

(16)

Before saturation ($D=100$%), a linear relationship describes this relationhsip. In particular, $D<50\%$ if $d<0.5$. Only the Somali translation is below this rather poor domestication index.

So far, we have studied how the original Greek texts were translated. The theory and analysis applied in this section, however, can be used to estimate how texts in any language might have been translated into any other language, similarly to what is shown for the so–called linguistic channels [2,3]. The next section deals with this issue.

6. Translation from Any Language to Any Other Language

We have no direct translation of the NT books from a modern language to another one, for example, from English to Italian. Now, the question we wish to answer is the following: can we deduce the mathematical characteristics studied in the previous sections of this unavailable translation by considering the available translations from Greek? We propose an exercise that should give a possible answer.

In the example just mentioned, we assume that the Italian translation from Greek can be also considered as the translation (i.e., the target text) from English (i.e., the source text), and vice versa. Of course, with this hypothesis, we neglect the likely “noise” introduced by the two translations from Greek. In other words, we are not sure that an Italian translator would translate the English texts as they are now in Italian. Ours may turn out to be only a useful conjecture. This exercise, in any case, is useful because it can indicate how much a text can be confused with another text of different translation; therefore, in this case, the complement number to $D$ = 100% can be interpreted in this way.

Figure 9 shows the scatterplot of $D$ (%) calculated by assuming English or Italian texts (source texts) “translated” into the other languages (target texts). The results are quite different from those shown in Figure 7 concerning the translations from Greek. Now, some translations show a low domestication index and, hence, greater similarity. The minimum $D=14.90$% in English is given by French, a realistic and reliable indication of the strong connection between French and English, as already noticed. In Italian, the low value $D=10.93$% is found in Latin; this is not surprising because Italian is the Romance language that is more directly derived from Latin.

Table A2, Table A3 and Table A4 in Appendix C reports $D$ (%) for any translation, and Figure 10 shows the scatterplot between $D$ and $d$ by assuming any language in Table 1 to be that of the source text. English (black circles) and Italian (green circles) are explicitly distinguished to show a general trend: modern languages, for a given $D$, are closer than Greek.

Finally,

Table 4. Synthesis of domestication index, $D$ (%), in the indicated translations. The column $D=100$ gives the number of translations that do not overlap with the language indicated in the first column. The other columns, for the language indicated in the first column, list the languages whose $D$ is in the indicated range, and the language with minimum, $D_{min}$. In Latin, for example, 7 languages do not overlap; 7 languages overlap (Fr, It, Rm, Sp, Ge, Et, and Hn) in the range of $D<30$; and 5 languages overlap in the range of $30\le D\le 50$. The language with $D_{min}$ is Rm; the 18 languages not mentioned have $50<D<100$. The language that is mostly not connected with the other languages is Nahuatl.

	$\mathit{D}\mathbf{=}\mathbf{100}$	$\mathit{D}\mathbf{<}\mathbf{30}$	$\mathbf{30}\mathbf{\le }\mathit{D}\mathbf{\le }\mathbf{50}$	$\mathbf{Language} \mathbf{of} {\mathit{D}}_{\mathit{m}\mathit{i}\mathit{n}}$
Greek	18	−−	Sm	Sm
Latin	7	Fr, It, Rm, Sp, Ge, Et, Hn	En, Fn, Sw, Ar, Sm	Rm
Esperanto	17	Al	Wl	Al
French	13	Lt, It, En	Rm, Sp, Fn, Hn, Sm	En
Italian	9	Lt, Fr, Rm, Sp, Ge, Et, Hn,	En, Fn	Rm
Portuguese	9	Dn, Ic, Cr	Ge, Bg, Sr, Rs, Et, Hn, Ar	Ic
Romanian	7	Lt, It, Sp, Ge, Et, Hn	Fr, En, Rs, Ar	It
Spanish	9	Lt, It, Rm	Fr, En, Hn	It
Danish	14	Pt, Ic, Bg, Cr, Sr	Ar	Ic
English	12	Fr, Sm	Lt, It, Sp, Fn,	Fr
Finnish	10	Sw, Bs	Lt, Fr, It, En, Tg, Sm	Sw
German	10	Lt, It, Rm, Et, Hn	Pt, Sp, Ar	Et
Icelandic	10	Pt, Dn, Bg, Cr	Sr, Ar	Dn
Norwegian	9	−−	Sw, Et, Ar	Sw
Swedish	6	Fn	Lt, Nr, Et, Bs, Tg	Fn
Bulgarian	14	Dn, Ic, Cr, Sr	Pt, Uk, Ar	Dn
Czech	19	Si, Uk, Hb	Pl, Sr, Ht	Uk
Croatian	10	Pt, Dn, Ic, Bg, Sr, Hb	Uk, Ar, Ht	Bg
Polish	24	Sl	Cz, Hb	Sl
Russian	8	−−	Pt, Rm, Et, Hn	Hn
Serbian	14	Dn, Bg, Cr	Pt, Ic, Cz, Sl, Uk, Ht	Bg
Slovak	19	Pl	Sr, Uk, Hb	Pl
Ukrainian	16	Cz	Bg, Cr, Sr, Sl, Ht	Cz
Estonian	5	Lt, It, Rm, Ge, Hn, Ar	Pt, Sp, Nr, Sw, Rs	Hn
Hungarian	6	Lt, It, Rm, Ge, Et	Fr, Pt, Sp, Rs, Ar	Et
Albanian	19	Es	Wl	Es
Armenian	8	Et	Pt, Rm, Dn, Ge, Ic, Nr, Bg, Cr, Hn	Et
Welsh	26	−−	Es, Al	Al
Basque	14	Fn, Tg, Sm	Sw, Cb	Tg
Hebrew	25	Cz	Pl, Sl	Cz
Cebuano	18	Tg	Bs	Tg
Tagalog	16	Bs, Cb	Fn, Sw, Sm	Bs
Chichewa	27	Lg	−−	Lg
Luganda	25	Ch	−−	Ch
Somali	10	En, Bs	Gr, Lt, Fr, Fn, Tg,	Bs
Haitian	18	−−	Cz, Cr, Sr, Uk	Uk
Nahuatl	31	−−	−−	Lg

summarizes the main findings reported in Table A2, Table A3 and Table A4 in Appendix C. The deep connections among texts of the same language family are evident by looking at the column $D<30\%$. English, mathematically, seems to belong more to the Romance family than to the German family, very likely for the reason previously recalled.

In the next section, we further deepen the scattering of the vectors shown by the circles drawn in Figure 4, Figure 5 and Figure 6.

7. Deep–Language Expansion Factor

In Figure 4, Figure 5 and Figure 6, the radius of circles varies from language to language because of deep–language parameters scattering. It is an interesting exercise to study the ratio of the radii. Let ${\rho }_o$ be the radius of a reference language/translation, e.g., Greek, and $\rho$ the radius of another language. We define the deep–language “expansion” factor, $E$, with the following ratio:

$$E={\displaystyle \frac{\rho }{{\rho }_o}}$$

(17)

Notice that $E^2$ gives the ratio of variances.

Now, if the spread of two languages is identical, then $E=1,$ and there is no distinction between the scattering of two texts, as should be expected in a translation with no domestication.

Figure 11 shows the mean and 1–standard–deviation bounds of $E$ versus translation/language. There are significant variations around $E=1$. For the most diffuse language families, we get the following conditional statistics: Romance languages, $E=0.970\pm 0.113$; German languages, $E=1.099\pm 0.162$; and Balto–Slavic languages, $E=1.252\pm 0.203.$ In conclusion, the Romance languages are the least biased (closer to $E=1$) and spread, and the Balto–Slavic languages are the most biased and spread.

Table A2, Table A3 and Table A4 in Appendix C also report the mean value ($m_E)$ and standard deviation ($s_E$) of $E$ for each reference language. For example, if Greek is the reference language, then $m_E=0.564$ and $s_E=0.136$; for English, $m_E=0.927$ and $s_E=0.223$.

Figure 12 shows the scatterplot of $E$ versus $D$, assuming Greek (red circles), English (black circles), Italian (green circles), or any other language to be the reference (blue circles). We can see that (a) $E$ ranges mostly between 0.5 and 2 before saturation ($D=100\%$), and (b) $E$ moves away from 1 as $D$ increases.

Finally, Figure 13 shows the histogram of $E$ and its log–normal model (see Appendix B) for log–normal modelling), whose parameters (mean ${\mu }_E\approx 0$, standard deviation ${\sigma }_E=0.332$, median $M_{E,0.5}=1.000$, and mode $M=0.899)$ were calculated from the linear value $m_E=1.056$ and standard deviation $s_E=0.360$. It is interesting to note that $m_E-s_E=1.056-0.360=0.696\approx 1/\sqrt{2}$, and $m_E+s_E=1.056+0.360=1.416\approx \sqrt{2}$; therefore, the $\pm s_E$ range is between $1/\sqrt{2}$ and $\sqrt{2}$, and hence the ratio of variances ranges between 0.5 and 2. This seems to be a rather general result. The value found in [28] is well within this range ($E=1.245)$.

In conclusion, the expansion factor varies according mainly to language family and also within a language family. Modern languages are more similar to each other than they are to Greek.

So far, we have shown that the Greek NT texts are largely domesticated in modern translations and that modern versions of the same texts can be less domesticated. This finding is certainly justified, because the Greek texts are difficult to render in modern terms, as it is hard to translate them verbatim. To assess, however, how domestication can also dominate the translation of modern literature, in the next section, we examine a few examples taken from the English literature to show that domestication can prevail over foreignization, just like we showed with a sample from Italian literature [28].

8. Domestication of Modern Literature

To assess how domestication can also dominate the translation of modern literature, we examine, as examples, the translation of Treasure Island (R. L. Stevenson, published 1881–1882) and David Copperfield (C. Dickens, 1849–1850), two novels from English literature.

Table 5. Treasure Island. Total number of characters ($C)$, words ($W)$, sentences ($S$), and interpunctions ($I$); and mean value (left number of column, $<>$) and standard deviation (right number, $s$) of the deep–language parameters in the indicated versions. Notice that the values of $<P_F>$ and $<M_F>$ reported here differ from those reported in [5], because in [5], only sentences ending with full periods were considered.

Language	$\mathit{C}$	$\mathit{W}$	$\mathit{S}$	$\mathit{I}$	${\mathit{P}}_{\mathit{F}}$	${\mathit{I}}_{\mathit{P}}$	${\mathit{C}}_{\mathit{P}}$	${\mathit{M}}_{\mathit{F}}$
					$\mathbf{<}{\mathit{P}}_{\mathit{F}}\mathbf{>}\hspace{1em}\mathit{s}$	$\mathbf{<}{\mathit{I}}_{\mathit{P}}\mathbf{>}\hspace{1em}\mathit{s}$	$\mathbf{<}{\mathit{C}}_{\mathit{P}}\mathbf{>}\hspace{1em}\mathit{s}$	$\mathbf{<}{\mathit{M}}_{\mathit{F}}\mathbf{>}\hspace{1em}\mathit{s}$
English	273,717	68,033	3824	11,503	18.93  4.89	6.05  0.93	4.02  0.09	3.09  0.38
French	309,923	68,818	4054	11,443	17.80  4.08	6.11  0.80	4.50  0.14	2.88  0.33
German	349,955	72,119	4111	12,294	18.27  3.68	5.96  0.74	4.85  0.16	3.05  0.36
Italian	305,132	64,603	3805	10,077	17.92  4.33	6.52  0.86	4.72  0.12	2.72  0.37
Russian	265,428	54,142	5218	12,006	10.63  1.75	4.53  0.31	4.90  0.14	2.34  0.26

and

Table 6. David Copperfield. Total number of characters ($C)$, words ($W)$, sentences ($S$), and interpunctions ($I$); and mean value (left number of column, $<>$) and standard deviation (right number, $s$) of the deep–language parameters in the indicated versions. Notice that the values of $<P_F>$ and $<M_F>$ reported here differ from those reported in [5], because in [5], only sentences ending with full periods were considered.

Language	$\mathit{C}$	$\mathit{W}$	$\mathit{S}$	$\mathit{I}$	${\mathit{P}}_{\mathit{F}}$	${\mathit{I}}_{\mathit{P}}$	${\mathit{C}}_{\mathit{P}}$	${\mathit{M}}_{\mathit{F}}$
					$\mathbf{<}{\mathit{P}}_{\mathit{F}}\mathbf{>}\hspace{1em}\mathit{s}$	$\mathbf{<}{\mathit{I}}_{\mathit{P}}\mathbf{>}\hspace{1em}\mathit{s}$	$\mathbf{<}{\mathit{C}}_{\mathit{P}}\mathbf{>}\hspace{1em}\mathit{s}$	$\mathbf{<}{\mathit{M}}_{\mathit{F}}\mathbf{>}\hspace{1em}\mathit{s}$
English	1,468,884	363,284	19,610	64,914	18.83  2.50	5.61  0.30	4.04  0.12	3.35  0.33
French	1,700,735	366,762	18,456	54,770	20.21  2.62	6.73  0.49	4.64  0.08	3.00  0.26
Italian	1,596,684	334,864	18,919	52,367	17.97  2.27	6.42  0.39	4.77  0.10	2.80  0.26
Spanish	1,511,564	338,041	18,654	46,938	18.37  2.19	7.24  0.56	4.47  0.10	2.53  0.19
Finnish	1,764,033	295,564	19,614	65,270	15.25  1.67	4.55  0.18	5.97  0.14	3.36  0.28

report the main statistics of the English originals and the available translations (WinWord text files). The means and the standard deviations reported have been calculated by weighting each chapter with the ratio between its number of words and the number of total words to avoid short chapters weighing statistically as long ones. As mentioned in Section 3, means depend on how they are defined/calculated. We proved in [28] that the mean calculated from totals, the mean calculated by equally weighting chapters (i.e., if $N$ is the number of chapters, the weight is $1/N$), and the mean calculated by weighting chapters according to its number of words increase in the same order. For example, in Treasure Island, for $P_F$ (English), we get, respectively, $P_F=\mathrm{68,033}/3824=17.79$, $<P_F> =18.89$ and ${<P}_F> =18.93$. For David Copperfield, $P_F=\mathrm{363,284}/\mathrm{19,610}=18.53$, $<P_F> =18.67$ and ${<P}_F> =18.83$. Notice, however, that these values are very similar.

Already from Table 5 and Table 6, we notice large differences between the English text and its translations, depending on the language. Figure 14 shows, in the same normalized plane of Figure 3, Figure 4, Figure 5 and Figure 6, the geometrical representation of all languages. From these figures, we can see the striking difference between Treasure Island and David Copperfield.

The translations of Treasure Island are significantly closer to the original English text.

Table 7. Treasure Island. Domestication index, $D$ (%), in the indicated languages.

	English	French	German	Italian	Russian
English	0	33.54	47.08	53.74	100
French	33.54	0	23.04	28.16	100
German	47.08	23.04	0	13.82	100
Italian	53.74	28.16	13.82	0	100
Russian	100	100	100	100	0

and

Table 8. Treasure Island. Expansion factor, $E$, in the indicated languages.

	English	French	German	Italian	Russian
English	1	1.18	1.29	1.11	2.80
French	0.85	1	1.09	0.94	2.38
German	0.77	0.91	1	0.86	2.17
Italian	0.90	1.07	1.16	1	2.52
Russian	0.36	0.42	0.46	0.40	1

report, respectively, the domestication index ($D$) and the expansion factor ($E$). The most domesticated translation is Russian ($D=100\%)$, and the least domesticated one is French ($D=33.54\%)$, another confirmation of the similarity between English and French. Russian is clearly very different of any other language.

The alleged “translations” can show a different picture. For example, the least domesticated language for French is German, not English. Italian and German show the least domesticated index; in other words, they show similar deep–language parameters.

As for the expansion factor, $E$, Italian ($E=0.90$) and French ($E=0.85$) show the nearest values to unity compared to English. Russian, again, is very different compared to any other language.

Table 9. David Copperfield. Domestication index, $D$ (%), in the indicated languages.

	English	French	Italian	Spanish	Finnish
English	0	100	100	100	100
French	100	0	70.88	54.35	100
Italian	100	70.88	0	24.87	97.22
Spanish	100	54.35	24.87	0	99.94
Finnish	100	100	97.22	99.94	0

and

Table 10. David Copperfield. Expansion factor, $E$, in the indicated languages.

	English	French	Italian	Spanish	Finnish
English	1	0.86	1.02	0.92	1.50
French	1.16	1	1.18	1.06	1.73
Italian	0.98	0.84	1	0.90	1.46
Spanish	1.09	0.94	1.12	1	1.64
Finnish	0.67	0.58	0.68	0.61	1

report, respectively, the domestication index ($D$) and the expansion factor ($E$) for David Copperfield. Compared to Treasure Island, now the translations of David Copperfield are completely domesticated ($D=100\%)$ in any language.

The alleged “translations” can show a different picture. Finnish is practically totally domesticated in any language, and it is interesting to notice that the minimum domestication index ($D=24.87\%)$ is between Italian and Spanish. As for the expansion factor, $E$, Italian ($E=0.98$) and Spanish ($E=1.09$) show the nearest values to unity compared to English. Finnish is, again, very different from any other language.

In conclusion, in modern literature, domestication seems to depend either on the novel—see David Copperfield, whose English original is fully domesticated in any language—or on the translation language—see Treasure Island, fully domesticated only in Russian for every language.

9. Summary and Conclusions

We have shown that a geometrical representation of texts, based on linear combinations of deep–language parameters, allows us to calculate a probability of “error” that indicates how much a text can be confused with another. Based on this probability, the domestication index, $D$, measures the phenomenon of erasing the linguistic and cultural difference of the source text to make the target text more fluent for the intended reader.

Another useful index, the deep–language “expansion” index, $E$, measures the relative spread around mean values of two texts in their geometrical representation.

The geometrical representation allows us to distinguish language family. For example, we have shown that Latin, Italian, Spanish, French, and Romanian—languages belonging to the Romance family, all mostly derived from Latin—are close to each other.

Bulgarian, Czech, Croatian, Polish, Serbian, Slovak, and Ukrainian—all in the Balto–Slavic family—are also close to each other.

Other less spoken alphabetical languages are clearly distinguishable from languages of different families.

English and French, although attributed to different language families, mathematically almost coincide. This coincidence, and the small distance between English and all other Romance languages, is due to the fact that many English words and some sentences construction come from French and/or from Latin.

In modern literature, domestication seems to depend either on the novel or on the translation language.

In conclusion, the requirement of making the target text more fluent makes domestication a choice that is largely more prevalent than foreignization. Domestication dominates the translation of the NT books from Greek to modern languages, and also within modern languages.

With varying degrees, domestication seems to be a universal strategy in translation, so that a blind comparison of the same linguistic parameters of a text and its translation hardly indicates that they refer to each other.