![]() The code is on GitHub, and I’d love to see (and link to) anything that you might do with it.Įvery class I took to learn about curved spaces or general relativity gave me the impression that it’s a super-advanced form of calculus, with lots of “delta-epsilon” proofs. So I got to thinking, what if I write a program to directly interact with curved space? This article presents the result of that tinkering: a hyperbolic portal that runs in your browser (no need to download anything), intended to give you a direct experience of spatial curvature. I presented this explanation in a previous article on this website, but the “space-time as a sheet” metaphor is an old one that might only be helpful after a course in Riemannian geometry and another in sewing.Ĭomputers have no trouble imagining curved spaces, and multitouch devices such as iPads let the user engage the computer’s abstractions in a palpable way. When I talk about curved space now, for instance, I’m imagining the contorted fabric of a pair of pants I once sewed, and how they couldn’t lay flat. Even as I learned about these things rigorously, it irked me that I couldn’t visualize them.Įventually, I came up with ways of visualizing these things that made sense of them without doing too much violence to the underlying formalism. I spent a lot of time thinking about what it might mean for a particle to be both here and there, and how something as insubstantial as space could be bent up and stitched together. ![]() Before I studied physics in college, I was captivated by two of the things physicists talk about: quantum indeterminacy and curved space-time.
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