  Geographical research was successfully quantified through the quantitative
revolution of geography. However, the succeeding theorization of geography
encountered insurmountable difficulties. The largest obstacle of geography's
theorization lies in scale-free distributions of geographical phenomena which
exist everywhere. The first paradigm of scientific research is mathematical
theory. The key of a quantitative measurement and mathematical modeling is to
find a valid characteristic scale. Unfortunately, for many geographical
systems, there is no characteristic scale. In this case, the method of scaling
should be employed to make a spatial measurement and carry out mathematical
modeling. The basic idea of scaling is to find a power exponent using the
double logarithmic linear relation between a variable scale and the
corresponding measurement results. The exponent is a characteristic parameter
which follows a scaleful distribution and can be used to characterize the
scale-free phenomena. The importance of the scaling analysis in geography is
becoming more and more evident for scientists.
