hmm, the "forgetting inner coordinates" idea might be screwed up because of affine vs projective here... the imperfect functoriality of the process of taking the projective space of a vector space... or something...

but anyway... i'm idly considering the possibility that when we think of the g2 incidence geometry as that of "a fermion rolling on a projective plane of 3 times the radius", the projective plane in question can be identified with a grassmanian of the long root subalgebra... hmm, but there are two dual ones of those to choose from, and it seems inelegant to have to so choose...

hmm, remember that it's the g2 "line" grassmanian that's most directly related to the long root subalgebra... ?? ...