Nick writes:
> Make sure that you all process Byers's definition of
> ambiguity before you crank up your rhetorical engines
> too high. Unfortuately the definition was
> "below the fold" in my original message. Again, it is,
>
> "...a single situation or idea that is perceived in
> two self-consistent but
> mutually incompatible frames of reference."
As you may recall, Nick, I have been working for
several years now to elaborate a mathematical model
of ambiguity for applications in psychology (etc.),
largely inspired by various goings-on in the Kitchen
Seminar and SEC Forum, and in particular with our
various discussions about schematization and emergence,
Jaan's notion (in a paper with Emily Abbey) of
"emergence of meanings through ambivalence" (where
he, inadvisedly, uses "ambivalence" to mean
"ambiguity"...damned Estonophones), and your and
Jim's repeated pep-talks on "levels of organization".
I hope to have a manuscript ready by January 25 (the
deadline for submission to a conference for which
the subject *might* be appropriate), and will
circulate it to these lists when it's finished
or on January 26, whichever comes first. The
working title is "Stratified manifolds, finite
topological spaces, posets, and (in)decision
trees: Ambiguity as a mathematical foundation
for schematization in robotics" (hey, it's a
robotics conference, okay?). As the title
sort of gives away (but only to initiates),
one of my concerns is how it is that continuous
(and, incidentally, infinite) "manifolds" of
data/stimuli/worldstuff/what-have-you become
"schematized" by human consciousness (and
language).
I can assimilate Byers's definition (as just
quoted) to my general ideas by rephrasing it
like this: "ambiguity consists in subsuming two
(or more) self-consistent but mutually (more
or less) incompatible situations or ideas
into a single situation or idea". That is,
"an ambiguity between (or resolvable to)
A and B (and C...)" is a higher-level 'thing'
than A and B. (Notice that I have committed
a rhetorical move by suddenly introducing the
notion of "an" ambiguity. That's actually what
I prefer to talk about, rather than "ambiguity"
as a general ... what? process?) I admit the
possibility of an ambiguity existing between
*any* two 'things' (for a given person at a
given time).
What's important to me (and what I'm trying to
write this paper in such a way as to promote)
is the idea that an ambiguity between A and
B is a first-class object in its own right,
not some sort of derivative construction.
That's why I've (I think) coined the phrase
"indecision tree", by which I mean nothing
other than a "decision tree" in the usual
sense (a finite acyclic digraph [whose underlying
graph *may* be cyclic {i.e., in Jaan's language,
there *may* be--and often is--equifinality:
different paths to the same endpoint}]),
but viewed in such a way that the non-terminal
nodes are conceived of as "states of indecision"
(or ambiguity) and treated as first-class objects.
(Fence-sitters of the world unite!)
Why in the world are you going to Houston?
The Austin Lounge Lizards have a fabulous song,
"I'm Going Back to Dallas, Texas (To See
If Anything Could Be Worse Than Losing You)";
surely Houston *is* worse than even Dallas.
Lee
P.S. I see that I haven't said anything about
ambiguity *of* mathematics. That's because I
can't make much sense of Bohm's or Byers's
comments as quoted. Maybe I need more context.
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