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Let's say you were to to pick up a dictionary and look up a word in Chinese before the advent of any type of phonetic notation system such as Pinyin or Bopomofo. How would words in that dictionary be organized? Would you look up characters by radical? Would they be organized semantically? Did it try and account for China's massive linguistic diversity in any way?

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    Wikipedia has a good initial review. – bytebuster Dec 10 '13 at 4:02
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    Dictionaries published in Taiwan, like the Far East Chinese-English Dictionary, still list the characters by radical/stroke order. (To look up a character, you first isolate the radical, then count strokes.) If you know the pronunciation, there are pinyin and Bopomofo indexes that can be used, but the actual entries go by radical. Radicals are basically semantic in nature, don’t you think? – neubau Dec 11 '13 at 7:18
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    Pre-20th century Chinese dictionaries did have a system for indicating pronunciation – see the Wiki page on ‘fanqie’ about this. This was not how they were organized, although rime dictionaries like the Qieyun and Guangyun grouped entries by tone – books one and two were for level tone, etc. As far as linguistic diversity goes, the Qieyun is believed to present a compromise between northern and southern readings of the characters. This isn’t a surprise, since dictionaries are usually meant to set unitary standards rather than reflect diversity. – neubau Dec 11 '13 at 7:18
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Chinese dictionaries have arranged characters according to radicals for several centuries, then sorting on next level according to number of strokes. Works when you're looking for the meaning or pronunciation of a character you just saw. Some dictionaries and encyclopedias also attempted sorting by "theme": animals, plants, metals, etc. Of course, works only if you know a word and are looking for how it's written.

The canonical list of radicals is taken to be that used in the Kangxi dictionary, presumed to be one of the most complete dictionaries ever made on Chinese logograms:

https://en.wikipedia.org/wiki/Radical_%28Chinese_characters%29#History

For Japanese I can attest the problem is solved via kana: when searching the kanji for a word you know, they're ordered according to the sorting of kana (aiueo, ka ki ku...) . When you look instead for a character's meaning or its pronunciation, though, they also use the radical + number of strokes method. As a foreign learner, you're in for some surprises for some characters' official stroke steps are not what you could intuitively think of :)

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