Posted by
Steve Smith on
Feb 12, 2007; 12:57am
URL: http://friam.383.s1.nabble.com/Category-theory-Wikipedia-the-free-encyclopedia-tp523500p523510.html
Owen, et alii -
>
> Has anyone used this in complexity science work? Or semantic web
> work? Or anything else? :)
My colleagues at UNM... Tom Caudell (whom I believe you have met), Tim
Goldsmith (Cognitive Psychologist) and Mike Healey (Mathematician
retired from UWash) are using it to develop knowledge models from
expert elicitation. The methodology they are developing is essentially
(apologies to them for any mistakes I make) as follows:
1) Collect a set of potential "experts".
2) Interview them about the topic in question, primarily asking what
words (terms) they use ot describe the topic, think about the topic,
pontificate on the topic.
3) Pile all these terms on a big blanket out in the field on a windy
day.
4) Toss the terms in the air and let the wind carry away the
lightweight and trivial ones.
5) Sort through the remainders and join up synonyms .
6) Go back to the experts and ask them to rank the pairwise distance
between terms. (N squared!) One gets a fully connected graph.
7) Do some kind of normalization thingy amongst the results... call it
a numerical average for now.
8) Threshold the edges such that the graph no longer is fully connected
(black magic mojo).
9) Iteratively consult a subset ( the more cooperative ones?) of
experts on steps 7, 8.
10) Viola!
Although I am only peripherally involved in their discussions on this,
I believe:
A) 8) There are probably more advanced graph theoretic things to do
than simply threshold the weights... like collapsing cycles and/or
finding some heirarchy, and/or thresholding some more interesting???
derived measure than the simple, original weights... maybe...
B) 7) There are likely somewhat interesting things to do here,
especially to (later) place the different experts "point of view"
relative to the collective. There would seem to be a lot of soft
and/or unknown factors regarding the nature of the experts... etc.
I'm trying to converge my own less formal theories about Metaphor in
Information Visualization (formal analogy, etc) with their work, but
there is still a bit of distance (probably entirely in my lack of
understanding of the nuances of category theory). My now-30-year old
BS in Mathematics and Physics with a handful of graduate courses in
group theory and topology tossed on top for garnish serves me just well
enough to get in trouble...
I have been doing work in Visualization of Ontologies which also seems
to relate... I'm not sure anyone knows how to build an ontology
really... or how to describe the caveats and conditions surrounding the
Ontology. The Gene Ontology I have worked most with seems to have
plenty of anomolies of both history and of the compromises made to
bring it to a single, agreed-upon ontology...
It seems that most Ontologies, at least for the moment are going to be
self-organizing... that the only people both able and willing to build
such a huge abstract beast are those who will also use it...
One problem (in my opinion) is that it is somewhat of a "theory of
everything" so in some sense, all formal knowledge models can be
expressed in or traced back to category theory... so merely saying that
one is "using category theory" is not unlike replying to the question
"How did you get here?" with "I used a mode of transportation".
For example, at a meeting between Caudell and two of my more strongly
mathematically inclined colleagues last week, it was stated with
complete confidence and agreement around the the table that Formal
Concept Analysis is "just a specific use of Category Theory"...
> We've knocked around the term Category Theory a bit lately, so I
> started looking into it a bit. This seems to be a reasonable
> starting place:
>
http://en.wikipedia.org/wiki/Category_theoryWikipedia strikes again! I am constantly amazed at how accessible and
thorough technical information on Wikipedia is. I can't vouch for it's
accuracy (or thoroughness) in this case, but I am impressed at how well
these articles seem to summarize what I think I already know and plenty
I'm still trying to figure out.
And to make it even more interesting... isn't Wikipedia a
self-organizing ontology of everything? If one "labels" the links
used in Wikipedia to other Wikipedia elements with the verbs used in
the text, does that not begin to make an ontology?
Like the first line In Categories:
mathematics, categories allow one to formalize notions involving
abstract structure and processes that preserve structure.
We have a link between "Categories" and "Mathematics" and perhaps
(suggesting new links or topic are needed in Wikipedia) "Notions" and
"Structure" or perhaps "Abstract Structure" and "Processes", etc..
I look forward to the evolution of this discussion here (If I can even
keep up).
- Steve
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