@raprap,
Real world applications of math techniques for handling more than three dimensions would include things like linear programming and routing techniques for trucking lines wanting to minimize costs involved in routing trucks through multiple destinations.
The physical universe we live in only has the three dimensions we observe. You could claim that time is a fourth dimension and resolve problems involving those four dimensions, but it isn't physical and you can't "visualize" it.
You can draw stupid pictures to help grasp the math, but that isn't the same as visualizing something.