Is it possible to translate a piece of language into your own without knowing the language? I understand the the texts within the Voynich Manuscript are of an unknown language, and yet cryptographers are still working on it and still trying to decipher it. Does that mean that it is possible to crack any piece of writing even if it's in a language you don't know, and assuming you have no access to any tools that can translate the language?
For example, let's say I see a piece of writing in Arabic, which obviously has no cohesion to English. Is it possible to translate it just by working on that piece of writing alone without nothing else? If so how would I go about this?
A core assumption of natural languages is that conceptual frequency and the grammar to construct and articulate concepts is not evenly and randomly distributed; so pattern discovery can occur. 

However, two problems can quickly arise:


If the language sample (or collection of samples) is too small, the patterns may not be distinct and consistent. Cretan Linear A for example lacks a large enough corpus for robust patterns.
If you have a decent corpus with lots of patterns, say a 1GB block of natural language text, the language could still be hermetic. You may know how symbols relate and which should occur when but you would still need intense in-depth knowledge of the human brain to map each pattern to the most probable human motivation or abstraction. So the language would have be of human origin with no explicit intent to befuddle the uninitiated reader.


If I chose a novel in a language I don't know (say Russian) and converted it into Wingdings; my brain would still feel that the text "fits" my innate idea of written language without knowing why. Ilmari Karonen is correct that this problem is inherently cross-disciplinary.

The cryptanalytic curio is that a natural language isn't secure according to mathematical models but can still be completely unintelligible, thus serving the same outcome. This is a security-through-obscurity irritant that some cryptanalysts love to scratch. :-)

So yes, it is possible with the right provisos. If you can decipher a previously unknown natural language with a large corpus, yet disassociated from all other languages - you will probably win a Nobel prize in something.