> Clifford's Geometric Algebra enables a unified, intuitive and fresh perspective on vector spaces, giving elements of arbitrary dimensionality a natural home.

2 points by ngcc_hk 2 days ago | parent | context | prev | next [–] | on: Visualizing quaternions (2018)

Once you accept that imaginary number is not about a straight real number but a number about rotation. And you have two number that is not the same, living in different dimensions. One about straight line and one about rotation I.e.

X0 ops X1(another number system ) where X0, X1 is real

You then have complex number or a+ bi where i^2 = -1 And you can have split complex number a+bj where j^2 = 1 etc

The next move is not only the usual quaternions which one can, but to Clifford algebra

x0 ops x1n1 ops x2n2 ops …

xi is all real but ni is a different number system represent things not on the real number but a different and higher dimension object.

For example, the Clifford Geometry define the 2nd not a i or j but a plane, so you have

x0 + x1<plane> … and so on

with more high dimensional object (especially if one may say x0 is x0<line>).

Like complex number it simplify a lot of things. Spinsor would be easier to define this way say.

The first one that it is not that useful just different way of grouping. IaAware of this taking by both physics and computer people. But it is a total different way of looking and should have been taught in high school or at least undergrad. A bad cycle here. It has a lot of use to understand physics for normal people whilst the tensor …

Also her struggle with thinking about shift to another game engine. Unreal … too complex and Godot … to engineering … her remark basically said she may have to go back to game programming (to get a living).

Both honest comments and reflect hard reality.