Ok.

Let's talk about flat spacetimes, for simplicity. An element of it is (cdt,dx,dy,dz), another different element is (cdt',dx',dy',dz'). Are the two elements connected in some specific way?

mumble, mumble, mumble...

yes!

(cdt)^{2} - (dx)^{2} - (dy)^{2} - (dz)^{2} = (cdt')^{2} - (dx')^{2} - (dy')^{2} - (dz')^{2}.

That's the structure.