The 4th dimension is a function of space and time.
Lets call it n-dimensional space and matrices.
N-space can be thought of in any of these three ways:
1- as the set of triples where x,y,z represent real numbers
2- as the set of points in space
3-as the directed line segments in space based at the origin
The first of these points of view is extended from 3 to any number of dimensions. We define Rn where n is a positive integer greater than 3, as the set of all ordered n-Tuples. Rn is representing the space time function.
I wont get into the heavy mathematics of it but I will try and summarize it.
In our "real world" we go from r,r2, and r3 which seem normal and comfortable so what is the point of going to Rn because our "real world" is 3 dimensional not n-dimensional right!
The mathematical operations that leave behind unknowns and changing variables that have left us with no answer operate within Rn space time. They teach you that everything has definites but then give no explanation for the unknowns and indefinites.