Well, a new dimension corresponds to a new manufacturing process, with different inputs. As long as there is substitutability you don't have "true" innovation.

I am familiar with dimension reduction (proper orthogonal modes, principal componets, factor analysis...) and you're right, at some level the number of variables is a matter of choice. But you still have to be able to close the system of equations. You can always ascribe the effect of all the neglected modes to "noise", though.

We have met the enemy, and he is us — Pogo