Map

"Map" is another word for mathematical function.

A map is a two-dimensional representation of a three-dimensional space. The science of making maps is called cartography.

Introduction

Early maps were vague and there was often controversy as to where to centre the map - one world map, for instance, has Jerusalem at the centre.

Many maps have a scale, determining how large objects on the map are in relation to their actual size. A larger scale shows more detail, thus requiring a larger map to show the same area. Some, though, are not drawn to scale - a famous example being the London Underground map.

If the map covers a large area of the surface of a globe, such as the Earth, it also has a projection, a way of translating the three-dimensional real surface of the geoid to a two-dimensional picture. The most commonly used is the Mercator Projection; other popular projections are polar and a variety of equal-area projections.

The features shown on a map vary according to its purpose. For example, a road map may or may not show railroads, and if it does, it may show them less clearly than highways.

Maps can be political or geographical. The most important purpose of the political map is to show territorial borders; the purpose of the geographical is to show features of physical geography such as mountains, soil type or land use. Geological maps show not only the physical surface, but characteristics of the underlying rock, fault lines, and subsurface structures.

Many mapping projects have been carried out by the military. An example of this the British Ordnance Survey (now a civilan government operation).

Because maps are abstract representations of the world they are not neutral documents and must be carefully interpreted. It is, of course, this abstraction that makes them useful. Lewis Carroll made this point humorously in Sylvie and Bruno with his mention of a fictional map that had "the scale of a mile to the mile." A character notes some practical difficulties with this map and states that "we now use the country itself, as its own map, and I assure you it does nearly as well."

Electronic maps

For maps on a computer display, e.g. from the web or locally stored on CD-ROM or harddisk, zooming in means enlarging the scale, either by showing a smaller area in the same viewing window or by showing the same area in a larger viewing window, and one of the following:

replace the map by a more detailed one
enlarge the same map without enlarging the pixels, hence show more detail
enlarge the same map with the pixels enlarged (replaced by rectangles of pixels); no additional detail is shown, but, depending on the quality of one's vision, possibly more detail can be seen; if a computer display does not show adjacent pixels really separate, but overlapping instead (this does not apply for an LCD display, but may apply for a CRT), then replacing a pixel by a rectangle of pixels does show more detail.

Combinations are possible, e.g. the second applying for text and the third for the outline of a map feature such as a forest, a building etc. Also the map may have layers which are partly raster graphics and partly vector graphics.

For a single raster graphics image the second applies until the pixels in the image file correspond to the pixels of the display; on further zooming in, the third applies.

For a PDF-file typically the second applies. The increase in detail is, of course, limited to the information contained in the file: enlarging a curve it may eventually become a series of straight line segments, or other standard geometric figures such as arcs of circles.

A variation of the third possibility is that interpolation is performed.

Text is not necessarily enlarged when zooming in. Similarly, a road represented by a double line may or may not become wider when one zooms in. A variation of the first possibility above is that more text is displayed (such as more town names), but that for the rest of the image the second applies.

Other uses

Road map is also used metaphorically for a plan, for example "Road map for peace".
In first person shooters and other computer games "map" refers to the current territory (including buildings, entities, spawn points, etc.) as well as the objectives that must be completed. For example, the map "de_dust" in Counter-Strike includes the brushes, textures, bomb sites, spawn points, and backgrounds.
Songlines as maps in Australian Aborigine culture.

Links and references

References

David Buisseret, ed., Monarchs, Ministers and Maps: The Emergence of Cartography as a Tool of Government in Early Modern Europe. Chicago: University of Chicago Press, 1992, [ISBN 0226079872]
Mark Monmorier, How to Lie with Maps, [ISBN 0226534219]

External links

Multimap world atlas: on UK, US, Canada, Australia and Western Europe more detailed than the rest of the world
[1] - Microsoft/Encarta/Expedia world atlas, for North America and Europe to street level.
MapQuest: on US, Canada and Western Europe more detailed than the rest of the world
Yahoo Maps: on US, Canada, Germany, France, Spain, Italy
Yahoo Germany: on France, UK, Germany, Italy, Spain, Portugal, Austria, Switzerland, Benelux
[2] - ESRI atlas of the US
UT scanned collection: by the University of Texas at Austin
Example of legend (Cito-Plan city maps)