Hi everybody! I am new in this fantastic forum.
I have a question concerning the wonderful talk at SIGGRAPH2019 from Charles Gunn and Steven De Keninck.
What are the benefits of an explicit dimension with e0^2=0.
In Geometric Algebra over R^2 (with e1 and e2 as basis), i can define a bivector e1e2 for rotation, furthermore i can ad a vector to the bivector to build a nilpotent element like e0:=e1+ e1e2 with e0^2=0. So i need at least no extra dimension for mapping a vector along a straight line by an exponential function…
I guess the extra dimension simplifies other operations like the meet operation etc. Is there a simple mathematical argument for the extra dimension?