The question is about spatial dimensions.
It seems to me that every dimension adds something fundamentally new to space:
If you have one dimension, you have different positions and the ability to move an object (like a point). By adding the second dimension, the objects have the possibility to go around each other - they mustn't go through each other to change positions. The third dimension allows to tie a knot. Is there anything new like this if you add the fourth, fifth, ... dimension?