I believe “The Orb” is actually a concept that holds a lot of power on these forums.
It’s an idea that can easily spread and is enjoyed. If you look at memes on here right now, you’re constantly being forced to “ponder” (or think about) it, which isn’t even something I’m complaining about.
It can plant itself (at least temporarily) in your mind. Since it’s also associated with so many things (like wizards and fantasies), it can encourage you to think about things in a certain way.
Isn’t this a 2d sphere? (aka S^1)
Yes. I believe so. And thinking about the internal surface of a 3D, hollow sphere is a lot like pondering an Orb.
You can build up logic systems using set theory geometry inside your own head to “ponder the wizard’s Orb”. Pondering an Orb can in theory do almost anything a modern computer can do inside a well-educated scholar’s mind.
Lisp programming is almost directly based on these same concepts, which is why lots of early programmers loved it. They found it easy to visualise using stuff like comprehension of Escher-type geometrical spaces to make complicated computer simulations. Feel free to add on anything else you know about stuff like geometrical group theory, even if you think I’m wrong about this overarching stuff.
Geometries are a system of encoding conceptual information. You can see this if you know about things like a C2 rotation, which can be simulated on a computer.