My apologies Agustino, I didn't realize that. — Metaphysician Undercover

Ok, no problem :)

Which brings me to the OP question. What do people mean when they say things like "the math is not the world," "the map is not the territory," etc.? In one trivial sense this is, of course, true and undisputed: a theory, a model, is just a concept that we hold in our minds, it is not that which the concept is supposed to describe. — SophistiCat

The issue here I think, is that mathematics must be applied, in order that it may tell us anything about the world. This means that things in the world must be evaluated, assigned a mathematical value. If there is a margin of error, when we assign the mathematical value, such as that indicated in my earlier post, then the precision of understanding which we normally associate with mathematics is lost.

So for example, if we have a unit of time, a period of temporal duration, which we assign "1" to, such that it is one length of time, and there is a margin of error, then "1" in this situation is not really equal to "1". In this situation "1" is equal to every value within the range of that margin of error.

I'll go out on a limb and guess that any measurements that are fine enough to test the HUP will not be about macro impacts. — andrewk

The stability of atoms has rather significant "macro-impacts". And you can demonstrate HUP at home with a laser pointer and some aluminium foil.

I will have an infinite number of relationships that can account for the underlying structure of the two variables which have generated these facts. — Agustino

And despite this, we aren't exactly overwhelmed by competing scientific theories are we? It is trivial to write down endless ad-hoc modifications to our best theories, which will be empirically indistinguishable from the original. Why does no one do that?

Well, there are several reasons no one ad-hoc modifies theories, the most significant being that scientific theories are not models and they are not equations.

the most significant being that scientific theories are not models and they are not equations. — tom

Then what are they if they are neither models nor equations? :s