There's also some magic to the Universal Translator and Babel Fish: they perform zero-shot real time translation.
That is, they are able to translate (in all directions) novel languages that were not previously heard[0]. It is an open question, with likely a negative answers, that there is a universal grammar even among humans[1] (the definition itself is vague but even the most abstract version is suspect and highly likely to not be universal across species). I think no one will be surprised if it is always impossible to interpret an entire language based on only a few words (let alone do it in real time)
This isn't a knock down, because even a trained device is insanely useful, it's just a note about limitations and triage. This is awesome stuff and I can't wait for the day we have transnational headphones. It's an incredibly complex problem that I'm sure is not short of surprises.
[0] There are a few exceptions such as Star Trek TNG's episode Darmok, S5E2, where the Tamarians' language is unable to be translated due to its reliance on cultural references (the literal words are translated but the semantic meanings are not). It's a well known episode and if you hear anyone saying "Shaka, when the walls fell" (translates to "Failure") they are referencing this episode (often not using the language accurately but who cares (nerds. The answer is nerds)).
Can’t speak for ST, but did they ever say the babel fish understood languages it never heard before? I thought the galaxy was just exceptionally well-cataloged, given the HHG itself, and humans were hardly unknown.
The babel fish translated via brainwave energy and a telepathic matrix:
> The Babel fish is small, yellow and leech-like, and probably the oddest thing in the Universe. It feeds on brainwave energy received not from its own carrier but from those around it. It absorbs all unconscious mental frequencies from this brainwave energy to nourish itself with. It then excretes into the mind of its carrier a telepathic matrix formed by combining the conscious thought frequencies with the nerve signals picked up from the speech centres of the brain which has supplied them. The practical upshot of all this is that if you stick a Babel fish in your ear you can instantly understand anything said to you in any form of language. The speech patterns you actually hear decode the brainwave matrix which has been fed into your mind by your Babel fish.
“Now it is such a bizarrely improbable coincidence that anything so mind-bogglingly useful could have evolved purely by chance that some thinkers have chosen to see it as a final and clinching proof of the nonexistence of God.
“The argument goes something like this: ‘I refuse to prove that I exist,’ says God, ‘for proof denies faith, and without faith I am nothing.’
“‘But,’ says Man, ‘the Babel fish is a dead giveaway, isn’t it? It could not have evolved by chance. It proves you exist, and so therefore, by your own arguments, you don’t. QED.’
“‘Oh dear,’ says God, ‘I hadn’t thought of that,’ and promptly vanishes in a puff of logic.
“‘Oh, that was easy,’ says Man, and for an encore goes on to prove that black is white and gets himself killed on the next zebra crossing.
“Most leading theologians claim that this argument is a load of dingo’s kidneys, but that didn’t stop Oolon Colluphid making a small fortune when he used it as the central theme of his best-selling book, Well That about Wraps It Up for God.
“Meanwhile, the poor Babel fish, by effectively removing all barriers to communication between different races and cultures, has caused more and bloodier wars than anything else in the history of creation.”
I think idea of Babel Fish might encroach on the computational complexity limit in some sense. Imagine a future "Theory of Everything" book written in alien language. The book has total of 1 million characters across its pages where each character is distinct. Now Babel Fish must be able to "translate" such a language to English given its oracle like powers? Can it do the job?
While Arthur Dent does read some stuff throughout the series that couldn't possibly be in English like signs on an alien planet, the full nature of the babel fish is rather vague and we don't know if it would work that way. As far as I can tell, all the written text it translates for Dent is in the context of living civilizations so the babel fish has brainwave energy to feed into the telepathic matrix - presumably telepathically using the knowledge of nearby persons for the translation.
That said, given the Heart of Gold improbability drive, I don't think information theoretic violations are your biggest problems.
That is, they are able to translate (in all directions) novel languages that were not previously heard[0]. It is an open question, with likely a negative answers, that there is a universal grammar even among humans[1] (the definition itself is vague but even the most abstract version is suspect and highly likely to not be universal across species). I think no one will be surprised if it is always impossible to interpret an entire language based on only a few words (let alone do it in real time)
This isn't a knock down, because even a trained device is insanely useful, it's just a note about limitations and triage. This is awesome stuff and I can't wait for the day we have transnational headphones. It's an incredibly complex problem that I'm sure is not short of surprises.
[0] There are a few exceptions such as Star Trek TNG's episode Darmok, S5E2, where the Tamarians' language is unable to be translated due to its reliance on cultural references (the literal words are translated but the semantic meanings are not). It's a well known episode and if you hear anyone saying "Shaka, when the walls fell" (translates to "Failure") they are referencing this episode (often not using the language accurately but who cares (nerds. The answer is nerds)).
[1] https://en.wikipedia.org/wiki/Universal_grammar