Are Interpretations created in the mind or do they exist on their own?

A great philosophical rift opened between me and my wife last night as we lay trying to go to sleep.  I don't know how we didn't discover this sooner:  I am a true-blue, through-and-through metaphysicist while she is a staunch materialist. 

This argument got started while discussing possible interpretations of Rosenquist's "I Love You with My Ford" (pictured above).  I offered up that to me, it was a tripartite flag (in the style of Germany's) representing the nation of pop art. 

Then she said something, I wasn't really paying attention, but our conversation hit on the requisite salient points:

• my interpretation was silly;
• there is no correct interpretation;
• if we knew what Rosenquist said about this work it still wouldn't be the correct interpretation;
• there are a lot of possible interpretations;

at which point a point of contention arose:  how many possible interpretations are there?  She said something to the effect that as soon as someone thinks of one with their mind, there is born another interpretation.  I countered by saying that the interpretations exist before anyone even thinks of them.  Not only that, but there are an infinite number of interpretations.

She bristled at my theory.  She asked "how can an interpretation exist without a mind to think it?"  I said that "there were an infinite number of interpretations possible the moment it was created" which I later amended to "even before it was created there were an infinite number of interpretations."

Well, as you can see we were clearly going deep dish.  She stuck to her guns, I stuck to mine.  It was a long war of attrition, but we realized that she dwells among the world of tangible things while I am adrift in the world of ideas. 

No insults were thrown, except she called me "Platonic" which I took as a compliment, and I lovingly called her a "flesh-and-blood pragmatist wretch" and then we started talking about the chronology of the Indiana Jones movies somehow.

If you are curious as to the answer to the question contained in the title of the post, it turns out we are both wrong--interpretations are neither created in the mind nor do they exist on their own.  They are actually sentient (yet mindless) non-existential beings called Golliwogs that are invisible to all five senses and only can be briefly found in paradoxical situations such as double negative sentences (I do not not exist) and certain M.C. Escher drawings.