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 ...

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