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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?

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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.

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