For as long as I have known not very much about physics , experts have disagreed over the sign of the Minkowski metric: apparently particle physicists prefer +++- , relativists ---+ [Wikipedia]. An attempt to resolve the issue via geometric algebra, combined with an exotic experimental investigation into neutrinoless double beta decay ultimately foundered [Ber01]; passim. [ To conflate a metric with a Clifford algebra is in any case dubious, since mathematicians seem unable to agree on whether to associate +++- with Cl(3,1,0) or Cl(1,3,0) --- leading to confusion elsewhere in this area. ] My own less adventurous investigations encountered similar controversy over the signature for Clifford algebra tailored to 3-space Euclidean geometry: I unhesitatingly selected Cl(3,0,1) in order to retain positive magnitudes for all versors, whereas roboticists [Sel05] follow a preference of Ian Porteous for Cl(0,3,1) . [ This puzzled me until I realised that practical robotics can presumably find little application for an odd-grade versor. ] However, while contemplating the the computation of a versor X transforming one vector frame F into another G , I noticed what might just constitute a decisive practical distinction, at any rate between Cl(p,q) and Cl(q,p) --- when p (alone) is even, the sign of G = 1/X F X is switched by substituting for X its dual X~ !! [ Trivial example when p+q = 1 --- F = G = [e] , X = 1 , X~ = e ; in Cl(0, 1) we have 1/X F X = G , 1/X~ F X~ = -G ; whereas in Cl(1, 0) no versor transforms F to -G . ] At the moment any physical and geometrical significance of this is unclear to me. In particular, in Cl(p,q,r) when r > 0 duality is a much more delicate matter: indeed when all p,q,r > 0 , a consistent definition of the concept seems impossible to formulate. [ In this fashion I extricate myself from having to admit that perhaps Jon Selig was right after all. ] Can any physicists out there cast further light? Fred Lunnon https://en.wikipedia.org/wiki/Minkowski_space @book{[Sel05], author = {Jon.~M.~Selig}, title = {Geometric Fundamentals of Robotics}, publisher = {Springer}, year = 2005, comment = {ISBN 0-387-20874-7 ; includes Euclidean subspaces} } @article{[Ber01], author = {Marcus Berg and C\'ecile DeWitt-Morette and Shangjr Gwo and Eric Kramer}, title = {The Pin Groups in Physics --- C, P, and T}, journal = {Reviews in Mathematical Physics}, volume = {13}, year = 2001, pages = {953--1034}, note = {August, 2001; \url{arXiv:math-ph/0012006v1}},