The question may sound silly. If it is I'm sorry for it but I just couldn't find an answer anywhere else.
I have just learned about vector spaces and their properties and on the other hand have also started with Lagrangian mechanics. The author writes: "The configuration of the system of N particles, moving freely in space, may be represented by the position of a single point in 3N dimensional space, which is called the configuration space of the system."
My questions here are how is it possible for us to visualize the position of say 700 particles using just a single point in 2100 dimensional space? I cannot make any sense of it. Since there are no constraints, for every particle we are adding up 3 dimensions; What is the advantage in doing so?
And is this in anyway related to vector spaces?