  If in the Randall and Sundrum RS1 model the inverse of the compactification
radius, the AdS curvature scale, and the five and four-dimensional Planck
scales are equal in size, as is natural, then the warp factor at the location
of the low energy brane is of value 1/pi. So that all scales derive from
locations in the space, we identify the extra dimension with the infinite
covering space of the S1/Z2 orbifold. The extra dimension is then essentially a
series of connected line intervals, punctuated by branes. Scales on successive
branes in the extra dimension descend from Planck scale in a geometric sequence
of common ratio 1/pi. Evidence is provided for such a sequence within the
spectrum of particle masses, and of a second geometric sequence, of common
ratio 2/pi, which suggests that the AdS spacetime is six-dimensional and doubly
warped. The scales of the Standard Model lie at coincident levels within the
two sequences. A third sequence, of common ratio 1/e, provides a symmetrical
framework for the Standard Model and points to a warped product spacetime.
