It's not mysterious that negating the parallel postulate is consistent; you just have to divorce the axioms from their originally intended meanings, and realize

It's not mysterious that negating the parallel postulate is consistent; you just have to divorce the axioms from their originally intended meanings, and realize that they apply to other objects besides those meanings. It's kind of like this. A biologist independently discovers directed graphs, but refers to the nodes as "organisms" and edges as "parenthoods", and then spends five hundred years trying to prove that every organism has only finitely many parenthoods, thinking it must be true since it's obvious biologically! Without realizing that graphs are far more general and apply elsewhere. Arbitrarily defining 0^0=π would not be speaking nonsense, it would just be speaking a little arbitrarily. Nonsense would be defining 0^0=rainbow