Kent,
    The answers you get to your question will depend on the biases of
the grammarians who answer it. I think most would agree that the
participle in an absolute modifies the preceding noun and thus the noun
+ participle constitute the noun absolute. The differents in explanation
seem to be in what is, and what is not, an absolute, and in how they
functions. Most traditional grammarians noted that most absolutes
function as adverbs. (Modern linguists now call them "sentence
modifiers," but that raises another whole question.) Your question about
why it is called an "absolute" is interesting, and I do not claim to
have the answer, but it may be that the absolute is one type of
"absolutely" reduced clause construction. When they function as adverbs,
for example, they can be seen as reductions of subordinate clauses:

When Jeff the party, everyone became bored.
Jeff having left the party, everyone became bored.


 KISS grammar apparently differs from those of most of the modern
linguists (and from most members of this list), and instead goes back to
Curme who noted that absolutes can function as subjects, objects of
prepositions, predicate nouns. Thus, for example, in


Him being there made me sick.

"Him being there" would be a noun absolute that functions as the
subject. Some prescriptivists may claim that "him" should be "his," but
they are wrong. If you are interested in more about Curme's
explanations, see:

http://home.pct.edu/~evavra/kiss/wb/G11/IM_NounAbs_TN.htm

There you will find more about the KISS explanation, and also scans of
the relevant pages from Curme.

Ed V.


>I sent this question out to my colleagues on the English faculty here
a
>couple days ago. No one has responded yet, so I guess they don't know
>either! It's probably a simple answer. Any help extended to this
>simpleton will be appreciated.
>
>Kent
>
>*
>Does an absolute phrase function adjectivally or adverbially? Since
it
>usually contains a participle, I suppose one would think of it as an
>adjective... However, since it's modifying the whole sentence or
clause,
>couldn't it be seen to function in both senses? Is it the one kind of
>phrase without an "absolutely" certain function?
>
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