As another part of preparing for the digestion of the $latex E_8$ result, I need to talk about flag vareties. You'll need at least some linear algebra to follow from this point.
A flag in a vector space is a chain of nested subspaces of specified dimensions. In three-dimensional space, for instance, one kind of flag is a choice of some plane through the origin and a line through the origin sitting inside that plane.
Flagging and colossus convergence. The rectangle (2d) was a start for the learning algorithm (in 5d). And the flag was essentially a start for the rectangle.
