no, see, we're dealing with English here.
In English, a word essentially means what it is used as. If we can only use the word's original meaning, then most of our current vocabulary is messed up, including at least three words in your first paragraph.
I have NEVER heard "geek" used to describe a carnival performer except in the context of someone telling me that is the real meaning of the word. It is in fact, the LEAST real meaning of the word, because it is used so infrequently.
The only agreed upon part of the definition of the word by people who actually USE it is to imply obsession and expertise as I mentioned earlier (and which Stacer appeared to agree with, using the word "obsession" in her connotation). Generally, it implies the fields I mentioned earlier, with less emphasis on intellectual/academic pursuits than computer/technical pursuits.
Sorry about the spiel about how the circus performer is wrong, but I'm really sick of people telling me that it means that when it doesn't anymore. It did at one time, but then, at one time, "Thesaurus" meant "treasury," and by extensive use of metaphor, it came to literally mean a collection of synonyms. Anyway, it irks me that this definition even shows up except as a fourth or third meaning, when it is no longer used that way. It irks me even more than dictionary.com says it means "socially inept," though this definition is certainly used more often than "chicken head biter."