Thanks. Claude tells me the essense of this example is "the GA formula for rotation works in 4D (vs quaternions), and to do something like rotation in kD you need a tuple of two objects of different grades because cross-product is a hack that only happens to work in 3D because the high-grade object there is degenerate, and to do 4D special relativity you need 4D rotations".

Is this more or less in the right direction to keep exploring?