[Corpora-List] QM analogy and grammatical incompleteness

[Rob Freeman]

Ramesh,

Thanks for bringing this up.

On Thursday 15 December 2005 04:11, Ramesh Krishnamurthy wrote:
> Hi Jörg,
>
> >Could you tell us more about this?
>
> Not a lot, unfortunately, although your question
> has prompted me to find out more....*
>
> (I think it was) John Sinclair (who) once
> described lexis and grammar as looking at
> language through opposite ends of the same telescope...
>
> Somewhere or other, I picked up the idea that if
> lexis and grammar were looking at the same
> phenomenon (language) from different points of
> view, the dichotomy might be similar to one that
> has confronted physicists: looking at light as
> particle and wave at the same time.

Like Dominic I don't think the correct analogy would be between lexis and 
grammar. I think something of a "quantum quality" lies in our intuitions of 
both.

Personally I find a very strong analogy between different grammatical 
properties and different quantum properties.

For instance, famously, you can perfectly describe the momentum or the 
position of a particle, but not both at the same time. This is Heisenburg's 
Uncertainty Principle.

It is no use asking what the "true" momentum and position of a particle is. 
You can have and exact character in terms of position, or an exact character 
in terms of momentum, but not both at the same time. Heisenburg's Uncertainty 
Principle tells us descriptions of physics are necessarily incomplete (to the 
order of a small constant.)

I think the same is true for grammar. To describe a language (characterized as 
a corpus of usage) in terms of one set of grammatical qualities, you need to 
mix it up with respect to some other set of grammatical qualities.

Different descriptions capture different important properties, but no one 
description captures all important grammatical properties at the same time.

I think that is why we have not been able to find a single grammatical 
description adequate to all tasks. That's why machine learning always "fails" 
why we can never train speech recognition systems to an adequate (single) 
representation for phonemes, and why even human taggers fail to completely 
agree on the right tags (as much as 3% error even after negotiation according 
to Ken Church) let alone agree on a single tagset.

So it is not so much the fact of going from a continuous quality to a discrete 
quality which is interesting, it is the necessary incompleteness of 
description in terms of discrete qualities abstracted from a distribution 
which is where I think we should be focusing, in analogy with the Uncertainty 
Principle of physics.

Dominic, I have only read the publically available chapter of your book. You 
mention a "vector model" for quantum mechanics. Do you have anything on the 
Web which talks about that? I can only recall ever having met descriptions of 
QM in terms of functions.

I agree completely with your message, but would only add that while quantum 
analogies can be very informative for lexis, where I think it really gets 
interesting is in syntax, which responds very nicely to a kind of "quantum" 
analysis in terms of generating new quantum qualities (particles?), a new one 
for each new sentence.

-Rob