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@kram1032:  The notation portion here is mostly "much ado about nothing".  You need an expanded notation to formally construct, demonstrate a property, explain a concept, to look for "what I'm I missing here?" and to complete a derivation.  Otherwise you're going to be working purely symbolically.  The tuple notation simply fits my brain better...partly because I'm a programmer.  Still I'd do - standard 2D model: X = (s, v, b) = (s, (v_x,v_y,v_z), b).  Say ~X is grade reversal: ~(s,v,b) = (b,v,s).  Standard 3D model: (s, v, b, t) = (s, (v_x,v_y,v_z), (b_x,b_y,b_z), t).  Multi-vector algebra tend to have a fair number of null-vectors, so the form of say (s,0,b,0) jumps out at me faster.  If I were to start playing around with 3D conformal GA you couldn't pay be to write out all 32 terms.  Another potential benefit is when are are looking a different mathematical types, which are related:  say complex numbers and quaternions.  But seriously I can't see this sub-topic as being very important.

WRT: Quaternions - although they can be used to represent a 2D projective space, a 3D interpretation is much more natural (i.e. 3D bivector plus scalar).

  You're right.  :p