Transformations - Spatial Mathematics: Theory and Practice through Mapping - page 59

situations in which relations can be observed to be the underlying conceptual
force.
3.1.1.1 Postal transformation
A simple, convenient example often given to students studying functions for
the first time is the following postal example. Suppose one is given a set of
hard-copy handwritten letters in envelopes that are to be sent through the
conventional US Postal Service network by regular first-class mail.
• My letter can be sent to a single address (one-to-one).
• My set of three different letters can be sent to a single address
(many-to-one).
• My one letter cannot go to three different addresses (not one-to-many).
Some might argue that the invention of the printing press permitted one page
to go to many. Yet, there is variation from page to page—there are ink splat-
ters, broken type, and so forth.
Still others might assert that photocopying of a page will enable one letter to
go to many different addresses, as long as the original as distinct from the rest
is not included—hence the rise of junk mail. Someone else might argue, how-
ever, that any two photocopies differ from each other on account of diminish-
ing the amount of toner available for copies later in the process.
Further, if one considers virtual messages, rather than hard copy messages,
then a single e-letter can be sent to a single address (one-to-one), a set of three
different e-notes can be sent to a single address (many-to-one), and a single
note can go simultaneously to three different addresses (one-to-many). The
electronic revolution of our “information age” offers a true postal transforma-
tion from the functional to the relational.
Perhaps a common theme in all these refinements of argument will be that
to move from one style of mathematical transformation to another in the real-
world requires some sort of underlying real-world transformation through
invention, revolution, or other remarkable event. Hence, we argue that the
printing press, the photocopying machine, the computer, and e-mail were not
mere inventions but were transformational technologies. They transformed
workflows and processes in entire organizations and in the greater society.
Electronic journals, delivered over the Internet, take advantage of this one-to-
many relational capability.
3.1.1.2 Home ownership
As we look around our environment today, such as a typical community in
the United States of America, we see a variety of dwelling types and a variety
of dwelling ownership.