About the Taiwanese language
There is a common misconception that Chinese is one language with differing dialects. The truth is that Chinese makes more sense if considered as a language family, rather than a language on its own, much like the Romance family of languages from Europe. Just as French, Spanish, Portuguese, Italian, Romanian and so on all derive from Latin, so Mandarin, Cantonese, Wu, Min (the group Taiwanese belongs to) and more derive from ancient Chinese.
Taiwanese and Mandarin (the most widely-spoken Chinese language) are mutually unintelligible. Put a monoglot Mandarin speaker together with a monoglot Taiwanese speaker and the only way they will be able to communicate is by writing (presuming that they can both read and write). It is important too to note that this is not because written Chinese is some kind of universal language, but rather that written Chinese is actually a form of Mandarin learned by speakers of all Chinese languages. To continue the comparison with Romance languages, it's similar to the Middle Ages in Europe, when Latin was the only written standard used, and was shared across countries and people who spoke very different languages.
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