The brain more or less has a dedicated section(s) used for processing language, regardless of where the language comes from or what order the person learned them. It’s not like, for example, Thai uses one part of the brain and French uses another.
That being said, language is a lot like art. It’s not always the same from person to person, culture to culture, setting to setting. Your brain is a highly capable factory and though there is a main terminal responsible for language it might need to ask for assistance from other parts when trying to determine meaning and pragmatics.
Latest Answers