  The relationship between the foundations of mathematics and physics is a
topic of of much interest. This paper continues this exploration by examination
of the effect of space and time dependent number scaling on theoretical
descriptions of some physical and geometric quantities. Fiber bundles provide a
good framework to introduce a space and time or space time dependent number
scaling field. The effect of the scaling field on a few nonlocal physical and
geometric quantities is described. The effect on gauge theories is to introduce
a new complex scalar field into the derivatives appearing in Lagrangians. U(1)
invariance of Lagrangian terms does not affect the real part of the scaling
field. For this field, any mass is possible. The scaling field is also shown to
affect quantum wave packets and path lengths, and geodesic equations even on
flat space. Scalar fields described so far in physics, are possible candidates
for the scaling field. The lack of direct evidence for the field in physics
restricts the scaling field in that the gradient of the field must be close to
zero in a local region of cosmological space and time. There are no
restrictions outside the region. It is also seen that the scaling field does
not affect comparisons of computation or measurements outputs with one another.
However it does affect the assignment of numerical values to the outputs of
computations or measurements. These are needed because theory predictions are
in terms of numerical values.
