The London Underground: An Amazing Subway Simplification and Mathematical Solution for Travelers

The London Underground: An Amazing Subway Simplification and Mathematical Solution for Travelers

By Mr Ghaz, May 8, 2010

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The London Underground: An Amazing Subway Simplification and Mathematical Solution for Travelers

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Construction of London’s subway began in the 1860’s. Over the next 70 years, as demands for public transportation grew, the system developed haphazardly until by the 1930’s it had reached much the form it has today: a network as sprawling as the city it serves.

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Drawing the system on a map was feasible-but the map was almost impossible for users to follow. Planning a trip with it was about as easy as finding one’s way into and out of a maze-and more difficult if the trip involved changing trains.

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Then, in 1931, draftsman Henry C. Beck found a brilliant solution, which led to the London Under-ground map so widely used today. Whether he knew it or not, Beck was applying the principles of topology, an exotic branch of mathematics in which, for example, a doughnut and a teacup can be regarded as the same thing.

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Topologists say that any two objects are the same if you can take a model of one-made of clay-and twist and mold the soft material into the shape of the other without tearing of breaking the clay of making new holes in it. According to topologists, a teacup and a doughnut are the same because both have a single hole through them. The hole in the center of the doughnut is equivalent to the hole in the handle of the teacup; and a doughnut made of modeling clay could, with a little skill, be twisted into a passably realistic cup.

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Beck’s proposal for a usable subway map was to abandon the idea that it should be a literal representation of how the lines ran underground. Instead, it should show the relationships between the stations. After all, what the underground traveler needed to know was which station he wanted to get to and whether he needed to change trains.

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To make it easier to read, Beck also proposed enlarging the central, most complex part of the system in relation to the simple parts at the outskirts. And for further simplicity, he would use only horizontal, vertical, and diagonal lines to represent the routes.

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Revolutionary Designs

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The transport authorities were dubious, fearing that many people would find new design just as difficult to follow as the old one. But early in 1933 a few experimental copies of the new map were printed. They were an immediate success.

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The simplification of the London Underground map was not the only spectacular success for topology. It has similarly revolutionized the design of networks for electricity, water, and gas; for automated assembly lines; and for traffic control.

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Even the circuit diagram that accompanies a transistor radio is drawn according to topological principles. It may be meaningless to a layman, and look quite different from the mass of wires and semiconductors visible when the equipment is opened up, but the topological diagram conveys everything an expert needs to know about the relationship between the different components. And it makes a repairman’s task as simple as seeing where to change subway trains in London.

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