(New UPDATE: Read my brother’s wonderful discovery-tribute to the German language, even though it does make him break out in flop sweat and armbands.)
My brother, back in grad school as he approaches 50 (and feeling alternately exhilarated and ridiculous), is taking a crash course in reading scholarly German, than which nothing could be more insane. You could accurately translate every word in a passage of such German, painstakingly consulting an on- or offline dictionary (here’s an amazing one, by the way, which serves up all the alternative and idiomatic translations of any word you feed into it, complete with examples in vivo), and still not understand the logical links and interactions among those words engineered by German grammar. If you misread number, case, or gender, or overlook a little track-switching word like nur (only) or nicht (not) or sondern (which always works in harness with nicht to mean “not this, but rather that”), you could go in exactly the wrong direction.
Fortunately, my brother has a sort of tutor — me — at his fingertips, and I in turn have the indelible memory of three years of drilling in grammar by an actual German German teacher in my high school, W. Gregor Heggen (wow, never Googled him before, amazing how many people thank him for things like helping them learn Irish), overlaid by some experience speaking and reading the language, to draw on. (Hey, that was a lot like a sentence in German!) I’m subfluent, and I probably have to look up almost as many scholarly-vocabulary words as my brother; but I have a basic grasp of the underlying track-switching system, the rails of relationship beneath the freight cars of vocabulary, that weaves the structures of meaning in German. Getting just that basic grasp took all three years. When our teacher took eight of us teenagers to Germany for the summer of 1962, starting with a one-month family stay in his hometown of Paderborn, we all soon started speaking German, but I was the only one who spoke it grammatically, because I was the only one with three years under my belt. The idea of a crash course in German grammar boggles the mind.
I’ve seen three passages my brother had to translate, and they represented three very different kinds of German. One was modern and brusque, written in short sentences almost imitative of Hemingway English. One was pretentious and convoluted, exploiting to the full the German mind’s ability to put the forward progress of a sentence indefinitely on hold right before the consummating verb for an enormous, indigestible digression. (It gives an English speaker a case of linguistic blue balls that makes you go “hmmm” about German sexuality. It’s almost sadomasochistic, that withholding of the verb that alone will let you off the hook about what’s actually happening in the sentence. The English speaker has to plod around the digression in search of the verb, and perhaps the German mind does this too, but much, much faster, scooping up the whole digression as it goes in one deft pelican gulp.)
The third was a rather famous passage by the composer Arnold Schönberg. Here it is in German, and here’s an official English translation — which is a lot like and no smoother than the one my brother accomplished with a little remedial nudging from me. You’d think the Arnold Schönberg Center could have found a better translator, but that’s not the problem. The problem is that it is untranslatable. Rarely have I read anything in German so purely German, in that nearly every word of it falls either into a space between two English words or a space that encompasses two or three English words.
Take, for example, Geist, a cognate of “ghost” in English. (That remains a minor and archaic meaning in German; there’s a separate word for the spooky meaning of “ghost,” Gespenst.) In some contexts, it will be translated into English as “spirit;” in others, as “mind” or “intellect.” But in German, it encompasses both. They are not two different things. We need at least two words to approximate the German word — poorly. What does that mean? It means, I think, that in English we think of mind as a tool, mechanism, or process that assembles or manipulates parts of ideas, while spirit is sort of featureless and above all that. Mind is a factory, if an advanced one; spirit is a mist. But in German, you think with your spirit. Ideas are not something you assemble, they’re something you apprehend.
And here’s another one: Wesen. Literally Wesen means “being” — it even shows up doing scutwork in the grammar, where gewesen means “been.” On a loftier plane it means the suchness of a thing — what in English it takes four lines of Gerard Manley Hopkins to say:
Each mortal thing does one thing and the same:
Deals out that being indoors each one dwells;
Selves — goes itself; myself it speaks and spells,
Crying Whát I dó is me: for that I came.
UPDATE: Or, as Dr. Seuss put it —
Today you are You/that is truer than true./ There is no one alive/ who is Youer than You.
For a one-word equivalent in English, we have to say “essence.” While this is in fact the exact Latin equivalent — esse means “to be”! — it’s come to have a different connotation in English; it’s sideslid into the less essential realm of perfumes, oils, and flavorings, which were originally called “essences” because they were a thought to be a concentrate or emanation of the very being of a substance — the way it “selves — goes itself.” In German, however, that kind of essence isn’t called Wesen — it’s called Geist. As in Birnengeist, a very concentrated clear pear brandy. Which brings us around to “spirits.” … and on and on.
Not to study at least one second language is a pity. Other languages shine a different light on the world, showing up things that are really there that might remain dark in our language. (There’s sometimes a leap of recognition when you learn a word in another language — it has lit up and pinned down one of the many, many phenomena we all feel but don’t have names for.) They also shine a new light back on our language, helping us to find fossils and wellsprings that have been buried under the sediments of usage.
Other examples?
The Compulsive Copyeditor 
