Jaza,
Of course in maths, you can have an n dimensional system if you have n number of elements in your array. Don't forget in theoretical physics, alot of what is postulated may not be observed, and the number of dimensions has to do with making the equations fit. Yes there may be 16 for a theory, 17, 18 or more in others.
Yes, I agree, the act of observing changes the subkect matter as there isn't a so called "passive" observer. Refer to schrodiginer's cat. Isn't it amazing that the chinese "magic" has put this idea into practice. By altering their state of mind through meditation and training, they can manipulate the physical world in ways that seem contary to newtonian laws. Their chi based training may in fact hold the key in making large objects behave in quantum states, akin to Bose-Einstein Condensation, but in room temprature. That is just a guess.