Map Projections
Maps are metaphors for distortion and the Platonic chasm between ideas and representations of them. Out there in ideal world is a sphere with things at different places on it. But spheres are buggers to work with, and we can't readily make paper maps with the same curvature as the section of the earth they represent. So we stretch and distort this ideal conception of the world to make it fit on a flat piece of paper; we project the globe onto a flat sheet of paper. In doing so we create illusions, misrepresent the real world, and mislead the reader. There are many projections (functions mapping the sphere onto the rectangle), each with its own advantages and disadvantages.
The classic illusion is the size of Greenland on the Mercator projection, the view of the world we're all used to seeing. Greenland is not really bigger than the USA, it's just a byproduct of the function used to map each point on the sphere to a point on the page. The Mercator projection preserves angles, making it useful to navigators, but it does so at the expense of accurately representing areas.
Other projections, such as the Gall Orthographic, preserve area. There are all sorts of variations on preservation, as map makers attempted to get specific benefits or to approximate the benefits of both (angles and areas are preserved for a particular piece of the map even though they're inaccurate elsewhere). Projections are part of the cartographer's art, and are beautiful to contemplate.
For that reason, I commend to you A Gallery of Map Projections. For maximum pleasure you'll combine it with a trip through Wikipedia's entries on Equal Area projection and Mercator projection. Enjoy, and to the club of peoplel who can never again see a map without checking the fine print to see what projection it employs.
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This reminds me of Monmonier's "How to lie with maps" which covers the many ways maps, by definition, distort or manipulate reality in order to represent it.
http://www.amazon.com/gp/product/0226534219/
It's another hint that perhaps there is no human comprehendible objective reality - that we always introduce bias into everything we do, or percieve. (Sorry to get all philosophical, but you did throw down Platonic dualism :)
Like the t-shirt says-
"Preserve Area: Use Albers Equal-Area Conic"
(see http://www.gisnuts.com/ for more projection related apparel)
"Maps are metaphors for distortion and the Platonic chasm between ideas and representations of them."
This sounds like a great opening line for a book. The book would then go into discussion of how software is a representation of human / business / economic / scientific reality.
Then it would proceed to the next level, discussing an aspect of a new technology that bridges the chasm a bit more precisely than any technology we've had in the past.
The book would provide a history of the chasm, of the earliest attempts at mapping, at representing, at bridging the gap. Then it would illustrate recent mapping attempts that have proved promising. Then focus in on one or more current technologies. Then outline future possibilities, in effect creating an idealistic "map" that attempts to represent what future engineered maps may look like.
You guys looking for an author for such a book? Sounds exciting to me!
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ian [04.13.06 10:28 AM]
if you want to get really nitty gritty, explore the world (actually universe) of datum. In the US alone there are probably 1000s of different projections that take into account location of area to be mapped--ther are state plane coordinate systems (Alaska has 10!) and come in different flavors--1927, 1983 survey feet, international feet, meters, and it goes on...