4 ms·
> clearly It's mysterious because it is only clear in retrospect. The fact that you can negate the parallel postulate and get a system that is still self-consi
by dvanduzer 13y ago
> clearly
It's mysterious because it is only clear in retrospect. The fact that you can negate the parallel postulate and get a system that is still self-consistent is incredibly mysterious. This is what sets mathematics apart. We "make it up" like other human accomplishments, and yet we can't actually just make it up. If we arbitrarily defined 0^0 = π, we'd just be speaking nonsense.
- xamuel 13y agoIt'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
- sireat 13y agoWe are clearly into the http://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences http://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_... territory and why most mathematicians seem to be Platonists.