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the vast difference between the chinese system of writing and alphabets i'm used to brings to mind a question: is there a notion of linear ordering of chinese characters? are all chinese characters enumerated (to the layperson, i understand that they'd have to be numbered to be encoded)?

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There are a few possibilities; dictionaries usually go by (number of strokes in the radical) + (number of strokes remaining). Because there are too many characters, there's usually a phonetic-based system involved too (Pinyin, Zhuyin, Kana, and Hangul); those have internal sorting, and that can be used too.

This is all separate from, say, Unicode code point ordering.

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