In both English and Japanese, a “hard-headed” person is obstinate:
頭が固い (atama ga katai: obstinate, inflexible) head + hard
In English, having a soft head sounds worrisome, but it’s a plus in Japanese, because it means that you’re open-minded (the opposite of hard-headed):
頭が柔らかい (atama ga yawarakai: flexible (person); open-minded) head + soft
In at least one case, you can add a verb (rather than an adjective) to 頭が, producing a very positive expression:
頭が切れる (atama ga kireru: to be sharp, be on the ball, have a mind like a steel trap) head + to be able to cut
The word 切れる is the potential form of 切る (kiru: to cut), giving us “to be able to cut.” What can you cut with a sharp head? It’s a strange image, isn’t it, especially when you consider that the brain is soft and mushy, whereas the skull is rock-hard and round! And yet English speakers routinely call people “sharp,” as in, “She’s sharp as a tack.” In that case, I suppose English speakers see the brain as a sharpened pencil, ready to go to work. That’s definitely weird, but it makes more sense to me than “being on the ball” (wouldn’t that make you wobbly?) or having a mind like a steel trap (which makes you ready to catch raccoons, but is that what you want your mind to be doing?).
Then there are issues of how high to hold your head. This is tricky in both languages. To encourage someone to take pride (despite others’ scorn), English speakers say, “Hold your head up.” But a snob has her “nose in the air”; she has apparently exceeded the maximum allowable height for elevating one’s head.
In Japan, too, it’s easy to violate these rules. On the one hand, people associate arrogance with an overly elevated head:
頭が高い (atama ga takai: haughty) head + high
On the other hand, holding the nose high means a positive kind of pride:
鼻が高い (hana ga takai: proud) nose + high
So I suppose Japanese and English speakers have swapped ideas about what’s arrogance and what’s high self-esteem. When you go to Japan, remember to hold your nose high but not your head. Sounds like one of those impossible yoga instructions.
Japan, the land of bowing and hierarchy, has even further do’s and don’ts when it comes to positioning the head. If you admire someone, you lower your head in their presence, at least figuratively:
頭が下がる (atama ga sagaru: to admire greatly, salute (in admiration), take one’s hat off to) head + to lower
You lower your head and also take off your hat? Do you take off your hat because it would fall off during a bow? Or is it that Japanese people bow, and English speakers take off their hats? Yes, I think that’s how it works.
頭が上がらない (atama ga agaranai: to be no match for (e.g., outclassed in authority, strength or in debt to), be unable to act on an equal basis with) head + not to be raised
The word 上がる (agaru) has scads of meanings. Here, “to be raised” is the best match (appearing in the negative form). And now we’re no longer talking about lowering one’s head out of admiration and respect. Rather, this expression indicates a head lowered out of a sense of unworthiness.
Life is complicated, isn’t it? But it seems that once you have your head screwed on straight, things tend to fall into place.
