http://friam.383.s1.nabble.com/Category-theory-Wikipedia-the-free-encyclopedia-tp523500p523514.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_theory>
> Wikipedia 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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