So I just watched the TV series Rome and thought to myself, since the Gauls speak the Gaulish language and the Ptolemaic Egyptians speak Egyptian, how would the Romans communicate with them? Interrogate Gauls or negotiating with the Egyptians?
The show roughly covers the period at the end of the Roman Republic, though with some historical issues we can skip over. It's a drama so they get to take some creative license. That said, the linguistic situation isn't terribly off. I'll expand this into the later years a bit if that's alright.
There are a few things to understand about this period. First is the spread of Latin. By the end of the Republic, Latin had already spread throughout the peninsula as a lingua franca. While the societal elites may also have had working knowledge of other regional languages like Etruscan, for any official business Latin was already available, even outside of Rome proper.
Additionally, Greek still maintained a high status among upper class Romans, and it would not have been surprising to meet someone of the upper class using Greek as a language of diplomacy. This would be no problem when dealing with Ptolemaic Egypt since Greek was also spoken there. Even in the Roman Empire, Greek was a primary language for getting things done.
However, aside from Greek and maybe some Etruscan, by the time the Republic had ended you would not have found many upper class Romans learning any languages like Gaulish. The Gauls, meanwhile, would be learning Latin and it would be in Latin that things like your suggested interrogation would take place. By this point in time, the language education for the sake of accommodating communication was fairly one-sided.
Thus, for the most part, Romans could have done fine with just Latin and Greek, and later just Latin.
Finally, you should keep in mind that being bilingual is not that rare throughout history for the upper class, and in many cases even the lower class as well. Historically, a monolingual country with reasonable economic power is a bit of an anomaly.
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