Calvin Lin made a wonderful set explaining multiple dimensions. In the questions, the volume of a sphere with its radius in 4 dimensions was derived.
What real world applications are there for the concept of the 4-dimensional sphere? Many people throw around the idea of 11-dimensions in string theory, without really explaining the significance/involvement of the higher dimensions.
On Mathematics Stack Exchange, Calvin wrote that "Lots of branches of mathematics currently have no application in any other field or the real world. ... However, that does not preclude the possibility that someone eventually finds a relevance for it. Before the 20th century, Number Theory was considered recreations 'useless' math. It has since spawned a huge industry of security."
Are hyperspheres part of a branch of Mathematics with no current real world application?
Also, what are the implications (mathematical or real world) of finding an equation for the volume of the 4 dimensional sphere?