so what about "geodesically non-holonomic rolling" or something like that??

i've been describing the g2 incidence geometry as involving "a fermion rolling on a projective plane of three times the radius", but actually i'm not sure exactly which systems if any would deserve such a description. for example the way that i have the mathematica animation set up at the moment, you see the fermion roll off the edge of the hemisphere, and simultaneously reappear at the antipodal edgepoint, _without_ flipping its fermionic bit; but why shouldn't flipping it be another reasonable option? i guess that part of the point is that when you're already admitting "fermionic global non-holonomy" (or something) it tends to interfere with the decision as to what wrapping or unwrapping of the base space you're using... ??or something?? ??is there really some principled way to decided that the morally correct description is "the large ball is just projective while the small one is genuinely spherical, and the connection between their frames is fermionic"?? ??or something??

??what about the possibility that although "octonionic rolling" is the only ("ungeneralized"...??) rolling ball system with extra _continuous_ symmetry, there might be other such systems with interesting discrete symmetry, and maybe some interesting way to classify these, perhaps even in a way that places the anomalous g2 continuous symmetry of octonionic rolling in an interesting context??

??so what about the idea of a numerological investigation of invariant distributions on partial flag varieties of exceptional lie groups to see whether the numerology of the distributions might match that of any relatively obvious "naively geometrically natural non-holonomic distribution" such as, say, "a 4d ball rolling on a 3d plane" (in some sense... i'm vaguely imagining some sort of "cartanian rolling" along the lines of the "cartanian geometry" ideas that derek wise has tried explaining to me, though that might be somewhat overkill as well as not the only sort of possibility...)?? to what extrent might this (or something...) be ruled out by what some people know about "prolongations of graded nilpotent lie algebras" (or something like that...), or by the failure of g2 to fit into larger root systems, for example??

??so what's the long root subsystem of f4?? this being the only other root system with such a sybsystem, to speak of (??) ... what about whether this might give hints about some interesting "generalized rolling" interpretation of the f4 incidence geometry??

is it something like a2 X a2 ?? no wait, maybe it's so(7)... no, i guiess that it's obviously so(8)...

so what _is_ the numerology of the "4d ball rolling on a 3d plane" distribution??

??9d configuration space?? ... ??...

??so _does_ a ball have to overcome some sort of friction in order to spin rather than roll?? (or in addition to rolling??) doesn't really seem like it, intuitively... ??...

??so what about the idea of a 3d ball rolling on a 1d wire?? or something??

???so what about some sort of generalization of "legendrian submanifold" (or something) that would include smooth non-geodesic rolling trajectories of the octonionic rolling geometry? ... ??again i'm imagining some vaguely cartanian ideas here... ??... ??something about "torsoroids" and so forth??

??assuming for the moment that some idea of "cartan geometry modeled on a non-homogeneous space" makes sense, then consider the case where the automorphism group of the non-homogeneous space is "frobenius integrable" ... ??is the geometry then automatically flat?? or something??

??any relationship between "shield" (as in "wall of shields") and "hoops"/"gimbal rings"?? ??perhaps not, since a gimbal ring seems like an "extended material object with persistent individuality of each of its points" ...?? or something??