3 ms·
The modern meaning of "geometry" may not change, but cutting and gluing space definitely break Euclidean geometry, as in, specifically the one defined by Euclid
by jerf 1y ago
The modern meaning of "geometry" may not change, but cutting and gluing space definitely break Euclidean geometry, as in, specifically the one defined by Euclid. You can't break a mathematical system much harder than to kill it at the axiomatic level. 4 out of 5, if not 5 out of 5, axioms do not hold if you include portals. That's pretty dead.
- zenorogue 1y agoFor an analogy: an Abelian group is a structure in which four axioms hold. A non-Abelian group is a structure in which three of these axioms hold, and the fourth does not. It is not a structure in which some random proper subset of axioms holds, because such a notion would be useless. While structures where specific subsets of axioms hold (non-Abelian groups, semigroups, monoids, etc.) are useful.