??so.... trying to picture [the involutions giving different real forms of simple complex lie algebras] in terms of root diagram picture.... ??what about possibility that such involutions more or less correspond to ... ???nice ways of marking each a1 as being treated as either "compact" or "split" ?? ...??or something??? ??but then why for example does it seem like g2 has allegedly essentially just 2 real forms while b2 seems like it should have 3 ?? ... ???or something ... ??...

??what about something about second, "cartan" involution (corresponding to _maximal compact_ subgroup ...) on fixed lie subalgebra of first involution ???....

??hmm, so what about real forms of so(4) ??? .... something about so(3,1) vs so(3) X so(2,1) ?? and so forth ... ???.... ??also something about relationship to real forms of so(5), via "long root" relationship ??? .... ???.... and so forth ... ??...

??so what about so(3,1) as underlying real lie algebra of complex lie algebra sl(2,c) ?? ...

??hmm, so in general... ???the underlying real lie algebra of a simple complex lie algebra x is a simple real lie algebra?? and is a real form of the direct sum of two copies of x ??? so... ??to find the real forms of a semi-simple complex lie algebra it doesn't suffice to handle the simple factors separately?? ???but maybe "this is as bad as it gets" ??? ... that aside from the phenomenon we're sort of seeing here, it suffices to handle each factor separately ?? ...

??so am i claiming here that when you re-complexify a complex algebra (or something...) you get it's "double" or something ?? ...??is there some obvious argument for that?? ...

???hmmm... ??is "involution" really an appropriate name for what i meant to be talking about here ?? .... ????.....