Analysis of GIS Data by Simple Examination - Introducing Geographic Information Systems with ArcGIS - page 355

FIGURE 6-3 Early computers: abacus and slide rule
Some Implications of Discrete Representation for GIS
Because, with GIS, the world is represented in a discrete machine, everything a GIS tells you is an
approximation—sometimes a poor approximation—of reality. For example, a GIS may represent a
curving road by a series of straight-line segments, which are themselves represented by numbers. Sets of
numerical coordinates (x and y pairs) placed along the centerline of the roadway define the beginnings
and endings of the segments. The sum of the lengths of the segments will, unfortunately, underrepresent
the true length of the curving road. The degree of error may be reduced by using shorter, and therefore
more, segments, but the fundamental problem remains the same.
Further, the “real world” is virtually infinite in the level of detail that exists (look through a microscope
if you doubt this), while a computer store is finite, and in many ways, quite small—compared, say, with
what is in your own head.
How does a digital machine store information about a continuous environment? By digitizing—using
this term in the most general way. We describe the world with numbers—integers (such as 7 and 2383)
and “floating-point” numbers (such as 1.618034 and 6.626 times 10 to the negative 34th power). We also
use strings of letters and other symbols: A, a, B, #, %.
To even have a chance at being sufficiently accurate when we specify a location on the Earth's surface, we
need to use a lot of digits. For example, the location of a particular fire hydrant near Vancouver, British
Columbia, Canada, was reported by a GPS receiver to be 49.2773361 north latitude and 122.8793473 west
longitude. Since each decimal digit requires some two and a half bits, the resultant binary number can be
quite lengthy, especially when you must add more bits for the exponent needed for floating-point numbers.
The capability to represent very precise numbers is sometimes called double precision or extended