N dimensions can give you 2^N degrees of freedom. If you have 3 spatial dimensions x, y, z, then you can have 3 degrees of freedom by translation and scaling a

N dimensions can give you 2^N degrees of freedom. If you have 3 spatial dimensions x, y, z, then you can have 3 degrees of freedom by translation and scaling along those dimensions. You can also have another 3 degrees of freedom by rotation around planes x^y, x^z, and y^z. I'm not sure what degrees of freedom are represented by the dimensionless scalar and pseudoscalar x^y^z, but probably one of them is mana points, and the other is hit points. Two spatial dimensions give you two translation/scaling axes (x, y), one rotation (x^y), and one stamina points (scalar). A 4x4 transformation matrix has 16 values, suggesting 4 dimensions, but it doesn't have 16 degrees of freedom, because several values are constrained. Nine values have three degrees of freedom, three other values have three more, and four are fixed, with zero degrees of freedom. Those six degrees of freedom suggest three dimensions, where two of the potential degrees of freedom are ignored. So a higher-dimensional mathematical space can embed a lower-dimensional model, if the constraints are clever enough, and map the degrees of freedom onto the right dimensions or combination of dimensions. This might be useful for generating smoother animations using linear interpolation, or avoiding gimbal lock, or attempting to unify gravitation with electronuclear forces, or something else.