[Corpora-List] QM analogy and grammatical incompleteness

[Rob Freeman]

On Tuesday 20 December 2005 17:29, you wrote:
> 
> > Where does the QM analogy with grammar break down?
>
> For starters, ...
> the operators for conjugate pairs, such as position-momentum

I conjecture most grammatical abstractions are in such opposition to a greater 
or lesser extent all the time.

If you take the word associations observed in a corpus and cluster them to 
abstract grammatical category you find you can make no single complete 
partition. If you group word associations according to one abstraction, you 
mix them up wrt another, if you now group them according to the second they 
are mixed wrt the first, and so on. There are an almost infinite ways you can 
cluster distributional information, but you can't cluster it all ways at 
once.

You get the same problem when you try to cluster wave functions. You can 
cluster them according to frequency, or position, but not both at once, hence 
the momentum-position opposition.

This is the origin of Heisenburg's Uncertainty Principle. I conjecture it is 
also the origin of grammatical indeterminacy in language (and meaning.)

-Rob