Matter in Space

A new linear mapping of the linear vector space (LVS) of the octonions is suggested as an approach to the co-ordinatization of space-time. This approach resolves some perplexing issues concerning the validity of certain pre-metric notions of orthogonality and mirror symmetry. It makes explicit the tangent space extension of four-dimensional space-time that was alluded to earlier by the author [3] and shows that the null space component of the extended space can be related to ideas that were set out many years ago by H J S Smith.