My favorite argument in Differential Geometry was arguing that the L2 norm is closer than the Arc Length norm when a piece of flat paper is folded. The demonstration is to fold paper in half and poke a hold. Then separate the fold to have a gap.
The math of the situation is arc length can be shaped differently to change the L2 norm distance.
Flat versus level. Space is curved, what does a flat curve look like? QED.
Is the surface flat from the human perspective or flat on the astronomical scale.
BIRPA support creates research like this.
Movie night is happening.