  Scale is a fundamental concept that has attracted persistent attention in
geography literature over the past several decades. However, it creates
enormous confusion and frustration, particularly in the context of geographic
information science, because of scale-related issues such as image resolution,
and the modifiable areal unit problem (MAUP). This paper argues that the
confusion and frustration mainly arise from Euclidean geometric thinking, with
which locations, directions, and sizes are considered absolute, and it is time
to reverse this conventional thinking. Hence, we review fractal geometry,
together with its underlying way of thinking, and compare it to Euclidean
geometry. Under the paradigm of Euclidean geometry, everything is measurable,
no matter how big or small. However, geographic features, due to their fractal
nature, are essentially unmeasurable or their sizes depend on scale. For
example, the length of a coastline, the area of a lake, and the slope of a
topographic surface are all scale-dependent. Seen from the perspective of
fractal geometry, many scale issues, such as the MAUP, are inevitable. They
appear unsolvable, but can be dealt with. To effectively deal with
scale-related issues, we introduce topological and scaling analyses based on
street-related concepts such as natural streets, street blocks, and natural
cities. We further contend that spatial heterogeneity, or the fractal nature of
geographic features, is the first and foremost effect of two spatial
properties, because it is general and universal across all scales.
  Keywords: Scaling, spatial heterogeneity, conundrum of length, MAUP,
topological analysis
