04
Part I: GEBChapter 4

Consistency, Completeness, and Geometry

Breaking the system from within. Non-Euclidean geometry.

For centuries, Euclid's geometry was thought to be the only truth. Then, mathematicians realized that by changing one axiom, they could create entirely new, consistent worlds (Non-Euclidean Geometry). This chapter teaches us that 'truth' is relative to the system you are in. A statement can be true in one world and false in another, yet both systems can be internally consistent.

The Poincaré Disk

"Infinite space trapped in a finite circle. As you approach the edge, you shrink, never reaching it."

[ INTERACTIVE: MOVE CURSOR TO WARP SPACE ]