[Retra]

There's also a broader picture -- that this effect arises because we use discrete, independent words to describe inter-dependent phenomena. The concepts of momentum and position are not good 'factorizations' of reality, so trying to talk about it in those terms leads to structural problems when you increase precision.

It's the same kind of problem you get when you try to talk about objective/subject morality, or whether science can prove things.

Another example I give:

The Sun revolves around the Earth -- True from Earth's perspective. The Earth revolves around the Sun -- True from Sun's perspective. They both revolve around their center of mass -- True in Newtonian model. The both follow straight geodesics in spacetime -- True in Einsteinian model.

Everything is true in some approximation. The idea is to increase your precision so that you can find truths that incorporate more information and thus provide greater insight and generality. If your language doesn't have enough 'bandwidth' to carry the information of -- that is, mimic the structure of -- your experiences, you have to develop more structured abstractions, or you'll lose clarity and expressive power.

So, for instance, you wouldn't have to prove that unicorns don't exist: you just have to show that providing more specific information doesn't result in a lack of clarity in a general model. A theory of three-legged unicorns offers no advantages over a model of n-legged unicorns because unicorns don't exist.

But now I've gone off the deep end...

[darkmighty]

I don't position or momentum are bad descriptions of a system. Also, it's not "factorizing" the system into the two parts, since they are related by a transformation (i.e. they are interchangeable, doesn't happen in factorization). It's important to have a good knowledge on the subject before you try to interpret meaning of it and specially when you try to extrapolate the situation.

I'm saying this also because the initial analogy wasn't so strong to begin with. A bunch of incorrect analogies can build the wrong picture of a theory which is hard to get rid of people's minds. Which is why it's good to reason through principles and not analogies (analogies are useful for other purposes: building bridges between the understanding of two different fields. I believe -- and they're made precise and clear in their shortcomings).

[Retra]

Position and momentum are bad description of a quantum system precisely because they are not independent. This is not really a statement about physics, but about language. It just happens to apply to physics because the purpose of physics is to develop useful language. And we make a better description in this case by saying things like 'position-momentum', using an actual equation, or by using a different concept like energy or wave-vector. All of which are better than position and momentum alone.

The extrapolation here really has little to do with quantum physics. I am also using QM as an analogy for linguistics. The theme is about how language captures information and how information-processing systems select output based upon linguistic structure. It's a very young and poorly understood subject, so I don't think it's very likely to get good theoretical work in a forum like this. These are primitive times, after all.