Quote from nitro:
You hold an applied mathematics degree from the university of Chicago? This is rather surprising, as the university of Chicago has zero interest in anything "applied" except maybe on the medical side - it prides itself on theory.
But to answer your statement, in my experience, is that the answer is yes and no, simultaneously. The market is generally covariant to coordinates used to describe it's price on your manifold of choice, and therefore one description does not invalidate the other. It is akin to saying, I use a thermometer to tell me it is hot, and you use your skin to tell you it's hot. The temperature is the temperature, but you are using a human instrument and I am using a quantitative one. The temperature is the temperature regardless of instruments used measure it.
Your questions comes down to: what is the tensor (or fibration or some mathematical structure we have not invented yet) that gives the map from the intuition/experience coordinates to quantitative methods coordinates. Both methods ultimately exploit structure. If people knew that map, they would be more than rich - they would have won the Nobel Prize in multiple disciplines because it would unify in a single stroke many mysteries of the human brain.
nitro
your take on chicago is reductivist bullshit, but i like the rest of your answer. i doubt rosy2 will be able to follow it, though.