Geography Reference
In-Depth Information
in the surface of the CD is a “1” bit, while no hole is a “0” bit. Whether or not a hole exists in the CD is
determined by a laser beam in the CD reader.
(You can contrast this technology, called “digital,” with another technology, called “analog,” in which
the elements are not limited to two states, 0 and 1, but, as discussed previously, may have many more.
An example of an analog system is a music recording on a vinyl disk, where a wiggly grove in the disk
creates an equivalent wiggle in the speaker cone.)
Why do you need to know this rather arcane stuff? (“Hey, I just want the car to go when I push down on
the accelerator and stop when I press the brake. I don't care what makes it happen.”) You should know
because the “real world” is a mixture of continuous phenomena (water flowing in a river) and discrete
phenomena (number of people living in a school district). A computer can only store discrete values.
Therefore, results from analysis of GIS data that come from computer storage and manipulation may be
in error—by amounts that may make an important difference.
Continuous and Discrete Phenomena
For this subject you have to think somewhat abstractly. Consider any system you like.
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At any
distinct moment in time, the elements of the system may be characterized by an exact condition,
or “state.” The state may be viewed as the values of a set of variables, which could (practically or
theoretically) be measured. We can talk about those variables as being independent or dependent.
For example, if the subject under consideration is elevations of the Earth's surface, the elevation
of a point might be described by the dependent variable “height above sea level” based on the
independent variables “position coordinates” (e.g., latitude and longitude) and “time.” The terms
independent and dependent are a little misleading, because cause and effect is suggested, where none
exists. The idea is, rather, that we (independently) specify place and time, which corresponds to a
particular elevation. The answer depends on the specifications, but the place and time do not cause
the elevation.
(I should say here that the difference between discrete and continuous phenomena has been the
source for much debate in philosophy, mathematics, and physics for centuries. Look, for instance, at
Zeno's Paradox (check the Internet). At very small sizes, a mixture of the continuous and the discrete
apply to many phenomena. Electromagnetic radiation (e.g., light) comes both in packets (discrete
objects) and waves (continuous phenomena). In theory, every moving object has associated with it
a wave, called the de Broglie wave. It applies primarily to subatomic particles (e.g., electrons), but
one could calculate the frequency of a de Broglie wave for an SUV moving at 30 miles per hour. We
won't. Instead, my intention here is to illustrate the difference between continuous and discrete in the
practical, human-size world.)
So, a system (phenomenon) may be thought of as consisting of (or being in) a given state at a given
moment in time. Following are some examples.
Discrete: A chess game has each player's pieces on particular squares of the board after a particular move.
It does not matter, in terms of the game, where in a square a piece is. When the last piece was moved, the
path it took or the length of time required for the move is of no consequence.
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System: a collection of elements (things: objects, ideas, organs, equations, banks, planets, and so on) with connections
of some sort between (proximity, gravity, pedagogy, electrical, chemical).
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