Transformations - Spatial Mathematics: Theory and Practice through Mapping - page 62

born July 1, 1950, would have the same Michigan driver license num-
ber. The first position would hold the letter “S” from the last name;
the next three digits would be based on the first three consonants
(mth) in the last name; the next three digits would be based on the
first name (James), so about a third of the way through the three
digit numbers from 000 to 999—maybe somewhere in the high 300s;
the next three digits would be based on the middle name (Edward),
maybe in the high 100s; and the final three would be based on the
birthdate of July 1, so maybe about 500.
• In the past, there were stories of a local resident with two different
driver licenses under two different names, an impermissible one-to-
many relation.
• Marital relationships (men and women):
• One-to-one: One woman is married to one man (monogamy:
Customary practice in the part of world predominant in math-
ematical development).
• Many-to-one: Many women are married to one man (polygamy:
Known, but not customary; some examples exist in European his-
tory, in the idea of a harem, and in certain religions).
• One-to-many: One woman is married to many men. Various cul-
tural taboos might lead one to ask what kind of mathematics
would have been developed in the 20th century had it been done
so predominantly by a society in which fundamental societal rela-
tionships are one to many. The broader societal environment in
which mathematics develops may well influence what mathemat-
ics gets created. As our human environment changes, do you see
changes that might produce substantial shifts from one transfor-
mation to another?
Finally, we note that the ideas of one-to-many and many-to-one might be com-
bined, as many-to-many. From the standpoint of application and education
what is important here is to see that:
• In the world of GIS, all of one-to-one, many-to-one, one-to-many, and
many-to-many concepts arise in mapping;
• Thus, the world of mathematical education needs to respond by offer-
ing extensive training not only about “functions” but also about the
often neglected “relation.”
3.1.2 Geoprocessing and transformations
Contemporary GIS software contains small programs designed specifically
to deal with one-to-many situations. Attributes for mapped features, such as
whether streams are perennial or intermittent, or the depth and magnitude
of earthquake epicenters, for example, are stored in a series of tables in a
geographic database, or “geodatabase.” These tables can be related in several