I used to think I could imagine 4 spatial dimensions. It's just an extra direction, right? I know x, y, z... just pick some random direction and call it w, that's it, right?

Wrong.

Rotations. I never even considered rotations.

Y'know how in 3-space, we have 3 rotational axes: pitch, yaw, and roll? I thought this was because each rotational axis happens when you lock one of the spatial axes (x, y, or z) and then spin around it. I assumed that in 4-space, you'd have 4 rotational axes, because you have 4 axes to lock. Turns out, that's wrong.

Rotation, in fact, is not about locking 1 spatial axis, it's about *swapping* 2 spatial axes. When you yaw 90 degrees, you're swapping forward/back with left/right. When you pitch 90 degrees, you're swapping forward/back with up/down. Etc.

Because of this, in 4-space, there are 6 rotational axes: pitch, yaw, roll... and 3 other ones nobody seems to have names for. To unify these terms, let's talk about them in terms of which two spatial axes they swap. I'm gonna say x is left/right, y is forward/back, and z is up/down, like on a mill. I can then notate pitch as yz rotation, because it swaps y with z when you do 90 degrees of it. Yaw is xy, and roll is xz.

In 4-space, you have a 4th axis: w. So you get 3 new rotations (for 3 new combinations): xw, yw, and zw.

This golf game lets you rotate in 4 of them: xy, yz, yw, and xw. Roll (xz) stays locked (as in most first-person games), because that would put the ground beside you, which is very disorienting. wz *also* stays locked, because that would put the ground in the w axis, which you can't see, which would also be wildly disorienting.

I haven't figured the rest out, but if you like your mindhole ♥♥♥♥♥♥ in this sort of way, go buy this game. You literally just exist in 4 dimensions... and play golf. That's it, that's the game.

Very fun.