In general I share you skepticism about finding small world networks everywhere, it seems to have become quite the in thing. (I happen to know that there are more than 6 degrees of separation between myself and Julius Caesar.)
However, I wouldn't be too hasty to use ambiguity as evidence against a networked model of the lexicon. A good piece of work that analyzed this can be found in the PNAS paper of Sigman and Cecch: http://www.isrl.uiuc.edu/~amag/langev/paper/sigman02pnas.html Beate Dorow and I have worked on this over the years, Beate's dissertation and Chapter 4 of "Geometry and Meaning" summarize a lot of findings. During this time, I started referring to ambiguous words in graphs as "semantic wormholes" - the fact that "change" can refer to different things enables you to join very distant parts of semantic space in a couple of hops. Ambiguity actually contributes to the connectedness of the graph - the thing you have to give up is the notion of transitivity in relationships, or any kind of triangle inequality in measuring distance. Either you need to split all your ambiguous words into separate nodes in the graph, or alternatively, accept that if nodes represent words which are ambiguous, distances are not measuring anything like distances in a metric space.
This phenomenon is often used in making jokes, as your change example demonstrates.
Perhaps my favourite of these goes something like this: Eager Young Minister: "Day to day, I find all the inspiration I need in the words of John and Paul." Elderly Bishop: "I quite agree ... though in my old age I've also come to a fresh appreciation for the words of George and Ringo."
I like this one particularly because you have two semantic wormhole nodes pivotting in phase with each other ... though I suspect this analysis would rather ruin the joke for most people (which I why I put the joke first!)
Best wishes, Dominic
On Wed, Nov 12, 2008 at 3:51 PM, Albretch Mueller <lbrtchx at gmail.com> wrote:
> Even though small-world networks may suffice to model some network
> connections, in general and in particular regarding linguistics, I
> could simply see some, as they say, "questionable" issues regarding
> the relationships among words, in a dictionary or in corpora, as
> "small-worlds networks" and I would assume you mean the direct (,
> naive) and straight word-to-word immediate connection of words. Here
> are just two points:
> * researchers have long suspected that just immediate, consecutive
> immediacy does not best describe NLs even if text and talk are are
> sequential. This is one of the reasons why they use Syntax Trees
> * also, even if you would build a DS to describe the huge amount of
> Direct (or inverted) Acyclic Graphs (ADGs) sprouting out of and
> sinking into every word, many relationships stated and/or latent (yet
> describable) happen while communicating which are neither direct nor
> acyclic, e. g., jokes and metaphors
> The other day I saw a homeless person on the streets with a sign,
> that read: "I am like Obama, I want change."
> change as meant by Obama: in the US government/society
> change as it pertains to money: a small amount (a few coins) you may spare
> Now, this person was using more than just a sentence -language- to
> persuasively entertain a joke (, which could be read differently by
> different kinds of people) and the relationship he expressed was quite
> a bit more engaging than the Aristotelian, linear/proportional one in
> "the spring of life ..." referring to our youth ...
> How well -if possibly- would SWNs model these NL expressions?
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