Comment on Fuck geometry
OrganicMustard@lemmy.world 2 weeks agoIt depends which metric definition are you using. The one I wrote is a pseudo-Riemannian metric that is not positive defined. Normally physicists use that generalized metric definition because spacetime in most cases has a metric signature of (-1, 1, 1, 1). Points with zero distance are not necessarily the same point, they just are in the same null geodesic.
kogasa@programming.dev 2 weeks ago
You’re talking about a metric tensor on a pseudo-Riemannian manifold, I’m talking about a metric space. A metric in the sense of a metric space takes nonnegative real values. If you relax the condition that distinct points have nonzero distance, it’s a pseudometric.