Mathematical Translatology

This post is for people who are mathematically minded. If you're not one of them, then skip it.

In my early days in translatology (aka translation studies) I laboured in machine translation (MT). There I was fortunate enough to work for a while under a brilliant French computer scientist, Dr Alain Colmerauer. He had begun his career, like many French computer scientists, as a mathematician, and he'd become an expert in the hybrid field known as mathematical linguistics (ML). In particular he specialised at that time in a type of ML called transformational grammar (TG). There's an article on TG in Wikipedia. His application of TG to translation, called Q-Systems (there's an article on them too in Wikipedia), was an early example (1970) of mathematical translatology and remains one of the best ever.

You still need maths to work on the design of MT systems, but since the late 1980s the maths has changed radically and TG has been swept away by statistics. Still, from time to time I'm taken by a nostalgia for the old days of ML. And so I set to thinking recently about whether ML could be used to characterise not the translation of specific sentences or sentence structures – which is what we mostly used to do – but the whole of translation. This is what I came up with.

Let I1 be an idea or message, piece of information, emotional feeling, etc.
Let I2 be another idea or message, piece of information, emotional feeling, etc., that is the same as, similar to or different from I1.
Let L1 be a natural language.
Let L2 be another natural language.
Let E be the expression function by which any I is expressed in any L.
Let T be the relationship of translation.

Let ei be an expression (utterance, text, etc) that is a product of E: ei = E(La, Ix)
Let ej be another expression (utterance, text, etc) that is a product of E: ej = E(Lb, Iy)

If Ix = Iy and La = Lb, then we have a paraphrase and not a translation.
Otherwise:
If Ix = Iy, then ej is a precise translation of ei.
If Ix ≈ Iy, then ej is a paraphrastic translation of ei.

In either of the latter two cases, let's label the relationship as T(ei:ej).

The question of what constitutes precise and paraphrastic is too big to go into here. It leads to a whole literature on 'equivalence' in translation. For the moment it must remain a subjective evaluation.

So far so good and quite obvious, but let's go a little further.

Let us declare that the relationship T is ordered and reversible.
Then T(ei:ej) ≠ T(ej;ei) and Ta(ei:ej) => Tb(ej;ei).
The formula models a procedure that is widely used in certain fields of translation and is called back translation. It happens to be empirically testable using an MT system that operates in both directions. Why MT? Because that way we can be sure of the stability and objectivity of the translator's 'mind'.
Here's a test using Google Translate and translating between English and French.

Input 1: My mother has gone shopping and will not be back before lunch.
Output 1: Ma mère est allée faire du shopping et ne sera pas de retour avant le déjeuner.
Input 2: Ma mère est allée faire du shopping et ne sera pas de retour avant le déjeuner.
Output 2: My mother went shopping and will not be back before lunch.

The result is a paraphrastic back translation. (Went doesn't have exactly the same meaning as has gone, but the tense of the French verb est allée permits two possible translations into English.)

Let's now declare that the relationship T is transitive:
Ta(e1, e2) and Tb(e2, e3) => Tc(e1, e3).

Thus, according to Google Translate again, where L1 is English, L2 is French and L3 is German:

T1(My mother has gone shopping and will not be back before lunch, Ma mère est allée faire du shopping et ne sera pas de retour avant le déjeuner.)
and T2(Ma mère est allée faire du shopping et ne sera pas de retour avant le déjeuner, Meine Mutter ging einkaufen und nicht zurück vor dem Mittagessen sein.)
=>
T3(My mother has gone shopping and will not be back before lunch, Meine Mutter ging einkaufen und nicht zurück vor dem Mittagessen sein.)

That's another paraphrastic translation, but close enough to validate tbe formula. (The mistake in the German is Google's.) Incidentally this example models that if either T1 or T2 is paraphrastic (or both are), T3 will also be paraphrastic. This operation is all the more interesting because it models a common procedure which is usually called relay translation or relay interpretation and is in practice widely used, especially in literary translation and conference interpreting, where a work or speech is often translated through an intermediate language by a translator who doesn't know the source language. Surprisingly, though MT was used to test it here, it's not exploited in any of the MT systems I've tried.

Well that's enough for now. A complete description would require incorporating other factors such as pragmatics. Have fun over Christmas!

Image
Alain Colmerauer, Chevalier de la Légion d'honneur.

Reference
Alain Colmerauer. Les systèmes-Q ou un formalisme pour analyser et synthétiser les phrases sur ordinateur. Publication interne no 43. Université de Montréal, [Dép. d'informatique], September 1970. 45 p. "Ce travail a été subventionné par le Conseil National de la Recherche du Canada: ceci dans le cadre d'un octroi à titre personnel et dans le cadre du projet de Traduction Automatique de l'Université de Montréal."

Google Translate: the examples cited were obtained 24 December 2015.



NPIT3, Winterthur (near Zurich), 5-7 May 2016
International forum for Non-Professional Interpreting and Translation, the latest paradigm in translation studies. http://www.zhaw.ch/linguistics/npit3.