Doug pointed out, in response to yesterday’s post, that there are many possible surfaces with hyperbolic curvature in them here or there. This actually follows from my recent conversation with Vi. Even solid space itself can be curved, for as Einstein pointed out in his General Theory of Relativity, when a big object (like a planet or a star) gravitationally attracts things, it’s actually creating a complex distortion in the fabric of space-time in the vicinity of that planet or star.
So at different places in our own 3D universe, “flat” areas of space can actually have a slight curvature. Some places might look round, like a Reiman sphere, whereas others might be hyperbolic. It would be great to create a software design tool that lets you “dial in” a desired curvature at any point in space — creating a new kind of shape whose curvature changes from neighborhood to neighborhood of space.
If we had the freedom to play with this, imagine what kinds of virtual environments and architectures we could create!
My brother Mike sent Vi a response video to her doodles yesterday. It’s pretty clever, but some of the jokes are a little too fast to really catch. She posted it on her blog:
http://vihart.com/blog/another-math-doodler/