Measure Words and their English Analogue I was taught that the closest analogue in English of Chinese measure words are 'units', e.g. "a pile of wood", "a cup of water", etc.

What strikes me as a bit odd about this analogy is that the units in English add semantic meaning to the sentence (see paragraph below), whereas in Chinese, it seems it is just some formal 'rule'.  I find this particularly weird because Chinese isn't exactly a language with a lot of unnecessary morphemes floating about.  It seems more Chinese to me to say “一男人” as opposed to “一个男人”; the “个” doesn't really add anything to that sentence, so, in the spirit of Chinese, I feel as if we should drop it.

Of course, all this would be explained if it did in fact add meaning to the sentence.  In English, for example, we can say "a pile of wood", but we can also say "a stack of wood".  In both cases, we have three things:  the thing, the unit, and how many units, and the difference between the two is precisely the type of unit.  I've been taught, however, that in Chinese, every noun has one and only one correct measure word associated to it, and in particular, you can't make the analogous distinction between the two cases in Chinese.  Is that in fact incorrect, so that, in certain cases, more than one measure word makes sense for a particular noun?  For example, can I say both “一瓶酒” and “一碗酒”?  If it is correct, and one and only one measure word is correct for a given noun, why do they exist in the language at all (for reasons other than "It's just a rule.")?
I've been taught, however, that in Chinese, every noun has one and only one correct measure word associated to it, and in particular, you can't make the analogous distinction between the two cases in Chinese.


This is completely wrong. Measure words in Chinese do carry meaning, just like in English. 

Using the wine example, all the following are correct:


一瓶酒 (a bottle of wine)
一碗酒 (a bowl of wine)
一壶酒 (a kettle of wine)
一杯酒 (a glass of wine)
一滴酒 (a drop of wine)
一斤酒 (a jin (a Chinese unit, =0.5 kg) of wine)


Because wine is uncountable, the measure words are container names, or volume, or weight. 

For countable nouns, such as 'person', there are singular measure words and collective measure words (also known as group measure words):


一个人 (one person)
一群人 (a group of person)
一队人 (a team of person)
一大帮人 (a big gang of people)
一小撮人 (a small proportion of people (from a large group))


Even within singular measure words for the same noun, there are different focuses corresponding to different contexts, such as:


一堵墙 (literally 'a blockage of wall')
一面墙 (literally 'a surface of wall')


When you want to say the wall blocked the exit, you may choose 一堵墙挡住了去路, while expressing a wall-ful of photos, you may want to say 照片多得挂满了一面墙. Although in this case switching them is fine (still grammatical), it would become less consistent in inner semantics, hence less literary.