Parisi and Sourlas [269] have suggested that a Grassmann vector space of dimension*n*can be interpreted as an ordinary vector space of dimension –*n*. As we have seen in chapter 13, semisimple Lie groups abound with examples in which an*n*→ –*n*substitution can be interpreted in this way. An early example was Penrose’s binors [280], reps of*SU*(2) =*Sp*(2) constructed as*SO*(–2), and discussed here in chapter 14. This is a special case of a general relation between*SO*(*n*) and*Sp*(–*n*) established in chapter 13; if symmetrizations and antisymmetrizations are interchanged, reps of*SO*(*n*)