Is it true to say that geometry isn’t computable? You can symbolically compute geometry. You wouldn’t be able to compute the decimal circumference of a circle,

Is it true to say that geometry isn’t computable? You can symbolically compute geometry. You wouldn’t be able to compute the decimal circumference of a circle, for example, but you can represent it as 2pir in a symbolic system. You can then use that to do things like symbolically derive other geometric properties (e.g. surface area of a sphere). It’s not clear that the universe “computes” the circumference of a circle to infinite precision. The best candidate I can think of would be the event horizon of a black hole, which is not composed of particles as I understand it, but I believe the jury is still out on whether the Plank length means that the shape of such a thing is still quantized at some level. Plus, humans can’t compute pi either. We can conceive of it, though, and I don’t see an argument for why an AI agent can’t conceive of it too (or at least behave like it conceived of it).