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 ]