A Germanic Fly In Amber

I've been taking a German course over in Berkeley, and my memories of the difficulties are coming back, even if I like the language more than Mark Twain. Cases and genders are like bread and butter for me, but the truly bizarre feature of German is the Separable Prefix, a grammatical abomination in a linguistic Limbo between adverbs and prepositions. The infinitive of the verb "to call (on the phone)" is "anrufen", but "I call the doctor" is "Ich rufe den Artzt an." This example is not so bad, but a sentence with the verb "aufpassen" produces the bizarre sentence "Passen sie auf den alten Hund auf?", "Are you taking care of the old dog?" in which the last "auf" refers to the "passen" at the beginning and the first "auf" governs "Hund" - at least there are no reflexives combined with it!