There is much that is captivating about a Gothic cathedral like the famous Notre Dame of Paris. The beautiful stained glass and the lofty interior space must have been truly awe inspiring to the 12th century Parisian. They certainly are to me.
In this photo, you are looking at an innovation that allowed the soaring interior space and relatively thin walls. It's called "rib vaulting." It may look chaotic but it is in fact very carefully arranged. How did they figure this out? Mostly trial and error and amazing intuition. The medieval masons didn't have computer models or even sophisticated math.
Here's another tidbit about gothic cathedrals: they are held together by gravity, not the mortar between the blocks. The mortar is really just a spacer to keep the stories level. Ribbed vaulting like this would have been stacked on wooden supports until the top stones were put in place. Once complete, the support was removed and the ceiling stayed up on its own. Impressed?