#### Question of Translation

How can you convert a text like “Me Amor!” to “என் உயிரே!” [from Spanish to தமிழ்] ? Lets assume we have Spanish to English and Tamil to English translators [bidirectional with English] then we can convert Spanish to English then to Tamil. Likewise one can translate between any two languages from a clique of languages [so far as the clique is defined such that each language can be translated to at least one other language in clique].

#### Development – Theory

Language can exist as text (print/message/document) or speech (audio, conversations) etc. Ideas are represented in any language. Ideas originate from one language and move to another, or sometimes originate iñ many lañguages simultaneously. Ideas cañ cross from oñe language to añother via text or speech.

In mathematical terms if we write **L** as set of lañguages = { L_{1}, L_{2}, .. L_{n}} and then if we define each language as a tuple L_{i} = (T_{i},S_{i}) then we may further define mathematical function operating on text and converting it to speech as :

**TTS**_{i} : T_{i} -> S_{i}

we may define a function speech recognition as,

**ASR**_{i} : S_{i} -> T_{i}

we may also define a translation function as,

**TX**_{ij} : L_{i} -> L_{j}

Essentially what we can do is by representing the language as a node in a graph with two text and speech parts to it, we may connect these nodes to each other via the edges – functions – like ASR and TTS, and to nodes of other languages via translators function edge.

In a graph with only two languages [English, Tamil] with all edges representing functions like TTS, ASR within same language and functions like Translator between two languages (one for each direction) we see a graph like the following:

Fig. 1: Language transformation graph. Nodes represent languages and their components. Edges represent functions like TTS, ASR [for same language] and Translators [directional between languages]. Clearly we may see this is a directed graph with ability to go from a specific language to another language in text or speech or both forms, provided a path exists from source to target language. Using such a graph with no orphan nodes, we may have universal translation powers from language A to language B [so far as bidirectional connectivity is present with at least one neighbor].

#### Problems to Ponder

So the curious reader now having a background of representing the translation problem as a graph problem of reaching node B from node A, can use rich set of path finding algorithms and shortest distance algorithms may attempt to answer some of these questions:

- What is the graph criteria for a language to have no translations ?
- What is the graph criteria for a language to not be able to have virtual assistant ? [Siri, Cortana, Alexa etc.]
- Conversely, to 2, what is minimum criteria [necessary but not sufficient] to have a virtual assistant [that can speak and listen] ?
- Given two paths to translating from language A -> F, which are of two different lengths which one would you choose and why? Assume all jumps have a uniform information loss. What if information loss at each edge is non-uniform, how can you optimized such a problem ?
- How would you introduce a new language into this graph so that it maybe translated to all other languages [unidirectionally] ?
- How would you introduce a new language into this graph so that it can be bi-directionally translated ?
- How can you represent the transliteration function in this graph ?

Answers will be posted soon! Feel free to leave your comments in section below.

-Muthu