Why is the word "rang" in so many Korean names for things? Sarang Community Church, Hwa Rang Do, Arirang Market--what's "rang"?
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Actually, this is what Ask a Korean! is missing
compared to !Ask a Mexican! -- an awesome logo.
But as to your question, the Korean is afraid that his answer is a bit of a letdown -- the "rang"s that you identified are basically false cognates. They don't really have any meaning on their own, and even if they do, they have nothing to do with one another.
To be more specific, sarang is purely Korean word meaning "love," and it is not the case that sa means one thing and rang means another, like "lo" and "ve" in "love" do not have any independent meaning.
Hwarang-do is slightly different, because it is a Sino-Korean word. Sino-Korean words are basically Korean words derived out of Chinese, a lot like the way many English words are derived out of Latin. (More explanation about Sino-Korean words can be found here.) So in fact, hwa, rang and do in Hwarang-do actually mean something individually. Put differently, Hwarang-do is written in Chinese characters like this: 花郞道. Each Chinese character -- 花, 郞 and 道 mean something.
But this is not to say that the meaning of the composite word exactly equals the sum of the meaning of its parts. 花 ("hwa") means "flower," 郞 ("rang") means "young men" and 道 ("do") means "way." So the composite meaning is... "the way of the flower men"? (What the hell?) Actually, the actual meaning of 화랑 (= "flower men") is a group of young men in late 6th century in Korea, who were known for their mental discipline and a certain strain of martial arts (among other things.) So Hwarang-do is actually the martial art practiced by the Hwarangs.
(Quick side note: if you were thinking the term "flower men" sounds rather, um, alternative, you are not too far off -- there are some number of Korean historians who claim that Hwarang group is the first sign of homosexuality in Korean history.)
One thing to note is that rang here does not stand alone in the normal parlance. This is easy understand when compared to Latin-based English. For example, the word "circumspect" is Latin-based -- "around" ("circum") - looking ("spect"), i.e. "careful to consider all circumstances." But English-speakers use the part "spect" alone just to mean "looking." (Anglophones would say "Look at this," not "Spect at this.")
The last example -- arirang -- is actually very, very tricky. Arirang is a refrain in many of Korea's traditional folk songs. In fact, many of those songs are simply titled Arirang, and each region of Korea has a different kind of arirang. (Also, interestingly, the biggest propaganda show in North Korea is called Arirang Festival as well.) Arirang is a pure Korean word, so rang itself PROBABLY does not mean anything. But the reason why the Korean had to emphasize the word "probably" was -- no one knows for sure what arirang is supposed to mean. The speculations have gone all the way from a proper name of a valley to pain associated with childbirth. And those speculation tend to hyper-analyze each syllable in arirang, trying to extract any possible meaning that makes sense. In this context, some scholars contend that rang has an indepedent meaning, while other scholars disagree.
One more occasion you might hear rang in Korean is when it is used as a classificational particle indicating companionship. (More about classificational particles here.) For example, a sentence that says: 나는 영호랑 식사를 했다 [na-neun Young'ho-rang siksa-reul het-da] means "I dined with Young'ho." The rang in that sentence is attached to the person's name ("Young-Ho", a Korean boy's name that transliterates rather unfortunately) to signify companionship with the person. In other words, rang in that sentence means "with", but note that particles only carry a meaning when attached to a noun. (This is more fully explained in the link above.)
-EDIT 11/22/2010- The Internet, as the endless echo chamber, brings back the Mexican's coverage of the Korean's coverage of the Mexican's question, which was prompted by the Mexican's comments on the Korean's coverage on CNN. That's a lot of covering.
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