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What are Topological Maps?

Thumbnail image of Tubular FellsIn map making or cartography, a topological map refers to a map that has been simplified so that only vital information remains and unnecessary detail has been removed.  These maps lack scale, and distance and directions are subject to change and variation, but the relationship between points is maintained.

As outlined in other parts of this website, the most famous example of a topological map is the tube map of the London Underground designed by Harry Beck in 1931.  Beck used simple rules on his map with as many straight lines as possible with any changes in direction indicated by 45, 90 and 135 degree angles.  He also adopted clear symbols for the map so that it was easily understood and enabled passengers to negotiate the complicated tube network more easily.  Within months it was an immense success and has remained so ever since.  Beck's work has become a design icon of the 20th century as much as the Eames chair, Concorde or Mini Cooper.

A topological map is derived from the branch of mathematics known as topology and was first academically described in 1847.  The subject studies the properties of objects that do not change as the object is deformed, much as the tube map retains useful information despite bearing little resemblance to the actual layout of the underground system in real life.  In reference to the Tubular Fells map, however, some seasoned walkers will realise that the map does not follow the rules of topology in all instances.  This was in order to preserve the feel of a transport, or as in this case, a tube map like that found in London.  Some people familiar with the fells will notice some peculiar alignments and ordering of the fells.  This is part of the maps eccentricity and will provide hours of fun for those who feel moved to identify the map’s cartographic transgressions.

Three stages in developing the mapAs you can see in Fig.1, the real geographical positions of the various features are shown as found on an Ordnance Survey topographical map.  To some people however, such maps can appear complicated and much of the details can be distracting. The red lines which have been superimposed show the simple details of the fell names and ridges connecting the fells.  By looking at Fig.2 with the OS map removed you can see the features much clearer.  In Fig.3 the real relationships between the identified features have been simplified even more, but in the process has distorted the true relationships between the fells, ridges and lakes.  In the illustrated example, the Tubular Fells map implies you can walk via Gatescarth Pass to get from Branstree to Shipman Knotts.  However, this is not the true reality as you would also have to traverse Harter Fell and Kentmere Pike. 

It would have been easy to produce a true topological map of the 214 fells, like that in Fig. 2, but it was the opinion of the cartographer, that in order to give the map clarity and more importantly to keep it looking akin to a transport map similar to Beck's, as many contiguous lines had to be created as possible with the features following on, one after another like stations on a tube map.  If strict topological rules had been followed, the map would have looked far more complicated, less aesthetically pleasing and would have lost its appeal as a surreal transport system which was the original intended aim. 

It will be intriguing for the observer to attempt to find these discrepancies and debate with others about alternative layouts.  The final format and configuration of Tubular Fells was not decided immediately, but it was the end product of hundreds of hours work.