On the true fourth dimension - context:

ftp://gallenhenderson.com/images/personal 045.JPG

 

We are extremely limited in our perceptions; our senses enable us to perceive only a small fraction of phenomena.   When I was a Manhattan dog owner, I marveled at the world that my dog would experience each time we went for a walk.   He perceived so many attractive things and even scary things that were beyond my perception.  A dimension is distinguishable construct, such as weight, height, etc.   Einstein demonstrated that constructs such as time, height, or even mass are contextual and highly dependent on the frame of reference of the observer.    

The strange attractor shown above demonstrates that distinguishable constructs exist even in randomness.   Consequently, many such constructs have been identified, and there is no finite limit on the constructs that can be valuable given a particular application.