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Subject:Re: Definition of mapping? From:Ben Kovitz <apteryx -at- CHISP -dot- NET> Date:Mon, 28 Jun 1999 16:38:01 -0600
Geoff Hart wrote:
> In broad terms, a map is any abstract representation of the
> relationship (physical or conceptual) between two things that are
> physically different but conceptually the same. The geographical
> maps that appear in atlases are probably the most familiar form
> of map, and they represent the relationship between a
> two-dimensional image of the world (which shows mostly positions)
> and the complex, three-dimensional real world.
Just a little nitpick here: a geographical map doesn't represent
the relationship between the two-dimensional image and the
three-dimensional world, it *is* the two-dimensional image. The
relationship is more often called the "mapping", but of course
sometimes people say "map" for that, too.
And a super-nitpick: a mapping isn't the representation of the
relationship, it *is* the relationship. Some bits in a computer
might be a representation of the mapping. Strictly speaking, a
mapping is nothing more than a set of tuples (a, b) where each
'a' is from a set A and each 'b' is from a set B. Hence there
doesn't even have to be conceptual similarity. There's a mapping
from criminal offenses to minimum prison sentences, a mapping
from inventory items to prices, a mapping from street addresses
to houses, etc.
I was going to suppress that last nitpick, but actually, lack of
conceptual similarity is the norm in computers. A typical
mapping is the ASCII code, which maps 7-bit strings to
characters. Another is that when converting from a "legacy"
system to a new system, someone will probably need to document
the mapping from the data fields in the old system to the data
fields in the new system. And there will surely be frustrating
little places where the fields just don't line up. That's
because really, there are two mappings: old data fields to
reality, and reality to new data fields, and the the two sets of
fields don't map to *quite* the same slice of reality.
(If anyone knows any tips on documenting that kind of
old-data-to-new-data mapping, please post! I did that last month
and was less than happy with what I came up with.)
