I'm learning geometric algebra. There is a very simple statement which I think is wrong. But it must be right, because all the experts say so. Arrg! The only properties used are 1a = a1 = a aa = 1 if b<>a then ab = -ba Their claim is that abcdabcd = -1. Let's see: aa = 1 abab = -abba = -aa = -1 abcabc = -abacbc = ababcc = abab = -1 abcdabcd = -abcadbcd = abcabdcd = -abcabcdd = -abcabc = --1 = 1 But the experts say abcdabcd = -1. See for yourself at http://geocalc.clas.asu.edu/pdf-preAdobe8/ZBW_I_QM.pdf, eqn 10 and 11 This can't be. To reduce the 4D case to the 3D case there have to be an odd number of swaps. They are of opposite signs and nonzero. They can't possibly be equal. Elsewhere they say that abcabc and abab equal -1. ?