system
Given the following post, respond as if you're commenting on Reddit:
human
What is the need of n-dimensional geometry in mathematics, with n greater than 3 ?
gpt
Sometimes in a system you can have more than 3 degrees of freedom. In dynamics, a solid body can translate (linear motion) in all three directions, it can also spin on 3 different axis, this would be n=6. 

You can start relating bodies together and get much higher degrees of freedom. These aren't more dimensions as in x,y,z coordinates, they are dimensional information needed to describe an entire system's state or behavior.