  Four-dimensional spacetime, together with a natural generalisation to extra
dimensions, is obtained through an analysis of the structures and symmetries
deriving from possible arithmetic expressions for one-dimensional time. On
taking the infinitesimal limit this simple one-dimensional structure can be
consistently equated with a homogeneous form of arbitrary dimension possessing
both spacetime and more general symmetries. An extended 4-dimensional manifold,
with the associated spacetime symmetry, provides a natural breaking mechanism
for a higher-dimensional form and symmetry of time. It will be described how
this symmetry breaking leads to a series of distinct properties of the Standard
Model of particle physics, deriving directly from the natural mathematical
development of the theory.
