joe quickly gave the book to aaron

Thinking about the example we talked about on Friday,
I expanded it briefly in four "synonymous" sentences:

1. Quickly, Joe gave the book to Aaron.
2. Joe quickly gave the book to Aaron.
3. Joe gave the book quickly to Aaron.
4. Joe gave the book to Aaron quickly.

Now, despite these sentences all being adequately
represented by the same set of *triples* (just a moment!),
it's weird, but they do seem to mean, or imply,
slightly different things. For example, sentence 1
seems to suggest an external event prompting the action,
sentence 2 seems to suggest that Joe might be feeling
some strong emotion, 3 seems more emotionally dry,
and 4 might be read as being devoid of emotion.

Well, that's just me reading into it, of course. But a pattern
suggests itself: the further the verb is from the subject,
the less emotion implied in the sentence. (I'm CCing
Zoe to ask if she's heard of anything like this in the
theory of natural language?)

As for the triples:

A. JOE GAVE BOOK
B. GAVE TO AARON
C. GAVE QUALITY QUICKLY

The word "Quality" is just a Pirsigian introjection to
turn the pair "GIVEN QUICKLY" into a triple.

It is important to note that the "GAVE" in the second
two triples is the same "GAVE" that appears in
the first triple, i.e. to really construct this statement
sensibly in Arxana, one will need a little more
data, e.g.

D. A modified-in-middle-by B
E. A modified-in-middle-by C

If we wanted to go with a different representation
scheme, it just so happens that a triangle works
in this case:

T=GAVE
T1=JOE
T2=AARON
T3=BOOK

In more program-like terms: GAVE accepts 3 arguments,
the GIVER, the GIVEN, and the RECIPIENT. In general,
if F is a function that accepts N arguments, then we can
represent F as an oriented (N-1)-gon... or even the vertices
of an (N-1)-dimensional simplex, if we care to go that
route.

That's roughly how I wrote things in my "100 short examples"
of PlanetMath entries rewritten as pseudo-code, or in my
APM-Xi. That is, every definition or theorem was a "function"
that took in certain terms to which it added some constraints.

I continue to think that triples are a "nicer" way to go, however!

For exploratory purposes, it would be nice to see some of
those complex Polish or Latin sentences written up and
treated in this, or any other useful fashion.