I might need to given in and buy myself a standard game controller. I'm happy to absorb information from gamer world, but not at the cost of needing to get good at any particular current favorite. I grew up on Doom, Quake and that genre, following Valve into Half Life 2, but without controller or console. The other lineage I got immersed in was Myst, Riven, Uru, by Cyan in Spokane. I'm abbreviating of course, skipping over any arcade favorites such as Tetris.
Anyway, as a side effect of being a "professor of Quadrays" (nuts to talk about 'em), I'm piggy-backing on a Crescent City project to fund a wider variety of implementations, beyond my own. Today was our hour meeting with the developer and it was partly about how to express the idea of quad-thrusters, per the QuadPod, in our evolving QuadCraft environment.
Defining my terms: Quadrays are by some assessments a juvenile toy used by crazies who want to challenge the dominant paradigm, but I push them as a conversation piece, aimed at opening space in the philosophy of mathematics that's friendly to children, with a tip of the hat to Montclair State (a "philosophy for children" headquarters), but is even more engaging once you're thoroughly familiar with the XYZ apparatus.
That's a pretty big tent. A good portion of the n-dimensional conventions copy over, even if lose the distinction of being a Hilbert Space.
What's the difference between Reflection and Rotation? That's a deep one.
Your reflection in the mirror is not simply a rotation of yourself in that a "mirror you", walking around, would seem curiously reversed, compared to if you simply turned around and walked in the opposite direction. Side-by-side, you'd not be identical twins.
But with simple arrows, directional edges, without distinguishing characteristics besides tip, tail and body, we might find it easy to define only rotation, such that -x, -y, and -z are 180 degree rotations of x, y, and z.
Were we to forbid vector rotation, and accept only scaling (grow and shrink without change in direction), and tip-to-tail vector addition, then the x, y, z basis vectors would be helpless to add to any points outside the first octant, or call it (+,+,+), no matter how much the stretched. They need their negative twins to reach the other 7/8ths of space, the other seven octants.
If the above paragraph made sense, you're likely ready for Quadrays then.
The four quadrays, without need of rotation, only addition and scaling, reach all the points a full XYZ would reach, starting from the same center.
Linear combinations of the four quadrays, in other words, span XYZ space, where XYZ space is only spanned by its own x, y and z basis vectors if we re-introduce rotation (we never needed reflection), where rotation is, in effect negation (vector reversal).
The quadrays permit vector reversal. Negation is just fine. But it's a form of rotation and is not needed to span volume omni-symmetrically about the origin.
All the above yammering is incredibly boring not to mention hard to decipher if your focus is on getting on with some game. But then later in a math class you might have some controller-based kinesthetic experience thrusting through the quadpod's four thrusters, and that'd help bolster your appreciation for the diagrams.
So our project is to turn these quadrays into a component of the game world, without making them the whole point.
They'll be the point for a small minority maybe, of tourists, the ones I bring to the repo (on Github these days), as their tour guide.
I'm the professor of Quadrays, after all, who wants to show off how they're implemented.
