  Based on a discussion of the theory experiment connection, it is proposed to
tighten the connection by replacing the real and complex number basis of
physical theories by sets R_{n},C_{n} of length 2n finite binary string
numbers. The form of the numbers in R_{n} is based on the infinite hierarchy of
2n figure outputs from measurements of any physical quantity with an infinite
range (distance, energy, etc.). A space and time based on these numbers is
described. It corresponds to an infinite sequence of spherical scale sections
R_{n,e} (e an integer). Each section has the same number of points but the size
increases exponentially with increasing e. The sections converge towards an
origin which is a space singularity. Iteration of an order preserving
transformation, F_{<} or its inverse shows exponential expansion or contraction
of the space with the origin as a source or sink of space points. The
suitability of R_{n} space as a framework for inflationary cosmology is based
on a constant iteration rate for F_{<} and time dependent e and n=n(t). At t=0
all space is restricted to a region of scale sections R_{n_{0},e} with n_{0}
(small) and e\leq e_{0} (negative). Inflation, which occurs naturally, is
stopped automatically at time t_{I} by increasing n from n_{0} to n_{I}>>n_{0}.
Here n_{I} is such that the outermost \Delta scale sections of R_{n_{0}} space,
which are moving at velocities >c at time t_{I}, are contained in the scale
section R_{n_{I},0} of R_{n_{I}} space. This is needed if R_{n_{I},0} space is
to be similar to the usual R space. Hubble expansion and the redshift are
accounted for by a continuing slow increase in n. Comparison with experimental
data suggests that the rate of increase must be at least one n unit every 30-60
million years.
