A Tale of Two Maps - Dr. Asaf Degani 2013

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A Tale of Two Maps: Analysis of the London Underground “Diagram”

The London Underground Diagram’s use of a diagrammatic design is a good example of proper information organization.

By Asaf Degani

FEATURE AT A GLANCE: This article presents an analytical approach to the prob­lem of information organization, with special emphasis on diagrammatic design. The approach involves three levels: (a) abstraction of data into representational elements, (b) integration of these elements to create coherent structures of information, and (c) configuration of such coherent structures, through underlying order, into a whole. To illustrate this approach, the abstract map (the “Diagram”) of the London underground is analyzed, and the design techniques observed are brought to the fore. The article concludes with several principles that can be encapsulated as constraints for an algorithmic approach to diagram generation.

KEYWORDS: organization of information, diagrammatic design, map design, formal methods

I

n his illuminating and whimsical book,

How To Lie With Maps (1996), Mark Monmonier argued that, “A good map tells a multitude of little white lies; it suppresses truth to help the user see what needs to be seen. Reality is three-dimensional, rich in detail, and far too factual to allow a complete yet uncluttered twodimensional graphic scale model. Indeed a map that did not generalize would be useless” (p. 25). How do we, then, make useful maps and diagrams? How do we display a multitude of information about a (complex) system without rendering it useless?

Figure 1 (page 8) is a geographic map of the lines and stations of the London underground network circa 1932. For more than 50 years after the inception of the London railway and trolley network in 1870, the presentation of the London Underground map was geographic. In the early 1930s, London Transport, which operates the Underground, was losing money; passengers found it difficult to understand the network of stations and lines with the geographic map provided to them (Garland, 1994).

Figure 2 (page 9) shows the first abstract map of the same Underground system.

Since that initial breakthrough (circa 1933), abstract maps have become pervasive and well recognized for their ability to bring to the forefront what’s important and remove the irrelevant. In doing so, they change the way we view our world.

This article is an analysis of the abstract “map” of the London underground. It probes the main principles that guided the map’s revolutionary design, focusing primarily on how to suppress truth and how to generalize content. Along the way, it tells

the story of Henry Beck (the man behind the design), the evolution of the London Underground map, and some of the internal debates and design decisions that shaped and reshaped this world-renowned icon.

Mr. Beck’s “Diagram” When the first abstract map was introduced to Londoners in 1933, it was immediately received with enthusiasm; at last, there was a useful map they could understand and actually use. Passengers quickly nicknamed it the “Diagram” primarily because it resembled an electrical wiring diagram. This was no coincidence; Henry Beck, the originator of the map, was an electrical draughtsman for London Transport (Leboff & Demuth, 1999). At 29 years of age, with no prior experience in graphic design, Beck came up with the idea of simplifying and organizing the “vermicelli” network by transforming it into a strict straight-line form.

From 1933 onward, the London Underground Diagram maintained this unique diagrammatical form, and Beck was invited, as a part-time employee, to further develop and modify the design. By 1937, Beck had come to a casual (“gentleman’s”) agreement with London Transport: In exchange for transferring the copyright of his design to London Transport, he would be retained, as a commissioned artist, to conduct all alterations and future editing of the Diagram. At the time, he could not have imagined how this agreement would eventually come to bedevil his life.

Although Beck left some written details of his conceptual breakthrough, it is difficult to glean exactly what he was thinking and how he went about creating the Diagram.

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A Tale of Two Maps: Analysis of the London Underground “Diagram”

Figure 1. Geographic map of the London Underground railway network, circa 1932. Copyright TfL from the London Transport Museum collection. Reprinted with permission.

product and identify the techniques he used in transforming a geographical map to an abstract diagram. The framework for the analysis presented here is based on the work of Christopher Alexander on pattern language (Alexander, Ishikawa, & Silverstein, 1977) and his more recent “theory of centers” (Alexander, 2002a, 2002b), in which Alexander considers three main levels in the design of a visual artifact: (a) abstraction of concrete data to form representational elements, (b) integration of these elements to create coherent information structures, and (c) the configuration of such information structures to create a holistic pattern. (See Degani, Jorgensen, Shafto, & Olson, 2009, and Degani, Barshi, & Shafto, in press, for application of the theory of centers to interface analysis and design.)

Abstraction The London Underground system is made up of several railway tracks. (The system that we recognize today is actually a merger, established in 1907, among several rail companies that initially operated independently with some degree of competition.) Along the lines are two types of stations: (a) regular stations, which have only one line passing through 8

them, and (b) interchange stations, which have two or more lines passing through them. To get from one station to another in the maze of the Underground, one needs to understand how the lines intersect and which interchange station can be used to switch trains. Beck’s originality was his realization that the primary function of the “map” was to help travelers navigate their way inside the network; surface details and true correspondence with the real geographic world are only secondary (Woodcock & Davies, 1996). He understood that from the passengers’ point of view, the network could just as well be represented as an abstract “world.”

With the 1932 map (Figure 1) as his starting point, Beck began elongating and straightening the lines using only straight lines (see Figure 3, page 9). Adhering only to line orientations of 0°, 90°, and 135° resulted in a schematic network that was clear, elegant, and simple to understand.

As Figure 3 suggests, Beck began the task of placing stations only after coming up with his initial layout. The abstraction of the lines and stations from their geographic positions gave him considerable freedom, especially with respect to regular stations that are arranged monotonically. He denoted regular stations by a small square “tick,” which allowed him to fit

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A Tale of Two Maps: Analysis of the London Underground “Diagram”

Figure 2. Diagrammatic map of the London Underground railway network, circa 1933. On the right is a scaled comparison of the two maps.

Copyright TfL from the London Transport Museum collection. Reprinted with permission.

more stations into a small space (the tick could be shown on either side of the line). Interchange stations, where two and sometimes three (e.g., Charing Cross station) lines intersect, proved to be a much more complex task.

Integration Beck recognized early on that the placement of interchange stations was the key to the success of the Diagram (Garland, 1994, p. 22), and indeed, this task consumed much of his efforts over the years. He and others experimented with how to explain the intricacy of the interchange stations as well as how to show relations among a “complex” of stations. For example, consider the complex of stations consisting of the Liverpool Street, Aldgate, Monument, and Bank stations, termed the “Aldgate Triangle” (because of the shape created by the lines passing through this area in the original 1933 Diagram).

After the Inner (later renamed Circle) Line was introduced following World War II, and the Fleet Street Line (now Jubilee) was being considered for this area in the early 1960s, Beck set out to tackle the problem of coming up with a more

Figure 3. Beck’s original sketch for the Diagram. Adapted from Mr. Beck’s Underground Map (p. 16), by K. Garland, 1994, Harrow Weald, UK: Capital Transport. Copyright 1994 by Capital Transport.

Reproduced with permission of the publisher.

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A Tale of Two Maps: Analysis of the London Underground “Diagram”

Figure 4. Four solutions to the “Aldgate Triangle” complex, circa 1965. From Mr. Beck’s Underground Map (p. 69), by K. Garland, 1994, Harrow Weald, UK: Capital Transport. Copyright 1994 by Capital Transport. Reproduced with permission of the publisher.

suitable geometric structure to represent the intricacy of this complex. Beck invested unprecedented enthusiasm and eagerness in this and similar design problems, primarily because of his unique expertise and utmost commitment to the Diagram.

But there was also a darker side to his tenacity – his incessant desire to maintain sole control over the graphic design of the Diagram.

Figure 4 depicts a series of design sketches made by Beck in 1965, showing four different solutions to the Aldgate Triangle complex. What made this task challenging is that several lines share stations and tracks and that the Bank and Monument stations are connected by an escalator. In such complexes, solving the problem of one interchange station at a time was not necessarily the best approach. A better and more efficient approach was to consider all the stations that made up the complex as an integrated unit and only then begin to rearrange and align individual stations.

In Figures 4a and 4c, one can see that Beck tried to move away from his original triangular design (see Figure 2). Using a more rectangular arrangement, he attempted to convey that in the Liverpool Street station, for example, there is a dedicated ramp for each line and a passageway between them (Figure 4c). Note also the use of the “white line connector” to show how the rings (representing stations) are connected

through a tunnel. In Figures 4b and 4d, Beck kept the triangular presentation and gave up altogether on showing the schematic details of the ramps and tunnels, favoring a single ring to represent a station. Note also the four different representations of the escalator between the Monument and Bank stations and their vertical relationship (the actual escalator goes up from Monument to the Bank Street station).

This example portrays the enormous flexibility, afforded by “going abstract,” to shape and reshape such station complexes. The four solutions in Figure 4 are so visually different that sometimes it is hard to believe they all represent the same geographic area. Creating such “successful” abstract structures is no easy task. Some psychologists have argued that it requires a certain intensity and capacity to delve into one’s emotional depths (Jung, 1955/1972). Henry Beck apparently possessed an uncanny ability to create such abstract and highly integrated diagrammatic structures. He spent an untold amount of time working on these details, at times bordering on obsession.

There are several other such integrated complexes in the Diagram – in the Kings Cross/Euston station area, around Charing Cross station, and at Baker Street. Analysis of these complexes suggests that finding a solution involves creating a coherent abstraction from individual abstract elements;

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A Tale of Two Maps: Analysis of the London Underground “Diagram”

Figure 5. The 1949 Diagram showing a rectangular overall pattern. The Circle Line (yellow), which engulfs the central area, is shaped like a water flask. Reprinted with permission of the Transport for London Company.

that is, an abstraction of an abstraction. We define this task as integration - the process of molding several informational elements that are practically and/or conceptually related into a coherent structure to reveal meaningful interrelationships (Shmueli et al., in press; Barshi, Degani, Iverson, & Lu, 2012).

When one is creating coherent structures, each element not only has to stand on its own but also must support and, preferably, enhance other elements (cf. Bennett & Flach, 2011, chap. 11); the stronger the relationships and mutual support, the more potent the design (Alexander, 2002a, chap. 3).

However, it requires not only emotional sensitivity and a keen eye but also the steadfastness to work and rework the details (of stations, lines, areas, and complexes) until a good integration solution emerges. Beck had all these faculties and, indeed, came up with many integration solutions during his tenure as lead designer for the Diagram. But his passion for detail and insistence on having full stewardship over any graphic changes worked against him because, by 1959, after 27 years with the Diagram, London Transport had enough of his anxious control over the product. So when one of the organization’s public relations managers (Harold F. Hutchinson) came up, on his own, with a reasonably clear design, they felt

they could turn the page on Beck. With his brainchild put up for adoption, Beck entered into a protracted legal dispute with London Transport over ownership of the Diagram.

Configuration Configuration is the act of arranging all the informational elements and their structures to create a whole. It inevitably requires an organizing principle (or principles), either noticeable or hidden, which guides the designer in how to “hang” informational elements and structures. Notably, viewers of the Diagram immediately appreciate the strict adherence to the horizontal, vertical, and diagonal orientation that helps to shape the network. The Diagram also conveys a sense of symmetry: There is a horizontal symmetry axis along the Central Line. In later maps (Figures 5, above, and 9, page 15), a vertical axis can be seen. The symmetry is not totalitarian and harsh but, rather, somewhat imperfect yet comfortable (cf. Alexander, 2002a, chap. 5; notion of “local symmetries” in architecture).

The Diagram also exhibits a unique and apparent pattern in its center. Note in Figure 5 that the central area is encapsulated by a shape that looks like a bottle on its side (where July 2013 | ergonomics in design 11

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A Tale of Two Maps: Analysis of the London Underground “Diagram”

Figure 6. Deformation map showing the correspondence between Beck’s abstract map of 1933 (Figure 2) and Stingemore’s quasi-geographical map of 1932 (Figure 1). The joint reference points are Charing Cross and Hammersmith station.

the yellow Circle Line now runs). Dubbed “the water flask” by designers who worked on the Diagram, the neck of the flask points eastward, with the Liverpool Street, Aldgate, and Tower Hill stations as the “cap.” It serves as a “strong center” that attracts the eye and helps organize the space (Alexander, 2002a, chap. 5). Extending out from this center are several diagonal lines (see Figure 2). There is an energetic tension between this eastward-pointing water flask and all the outward lines extending both northwest and southwest, lending the Diagram a memorable impact.

Interestingly, during the period 1941 to 1959, Beck gave a more rectangular shape to these lines, which lessened this dynamic pattern (see Figure 5). He thought that elimination of the diagonals and adherence to horizontal and vertical forms would simplify the Diagram. But, in fact, this modification made the overall pattern less clear and not as dynamic and perceptible as his earlier designs.

This must have been a sore issue with London Transport managers, because immediately after Beck’s dismissal, the diagonals were put back into the Diagrams and the dynamic pattern that has made it a visual icon was restored.

Furthermore, in a 1964 version designed by Paul Garbutt,

a diagonal was added at the eastern end of the District Line from West Ham to Upminster, perhaps to strengthen and continue the diagonal pattern of the lines. Nevertheless, the actual geographical rail track runs in an almost horizontal line (see Figure 6). This deformation of the District Line, which has an appealing artistic flair, has been preserved to this day, as can be seen in Figure 9 (page 15).

The most radical configuration technique in the Diagram concerns the wholesale deformation of the entire London map. In the course of laying out his Diagram, Beck quickly realized that he needed a considerable amount of (Diagram) space to detail station complexes in the central area, whereas in the areas outside the city, he could shrink the lines. He capitalized on an interesting idea of one of his predecessors, F. H. Stingemore, Underground map designer from 1926 to 1932. In Stingemore’s map of 1932 (Figure 1, page 8), there is a slight artificial expansion of the central area, most likely in response to the public’s continual difficulty in reading the map (Garland, 1994, p. 13).

The extent to which Beck expanded on Stingemore’s idea can be seen in Figure 6. The figure illustrates the amount of deformation in the Diagram by means of an arrow that

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A Tale of Two Maps: Analysis of the London Underground “Diagram”

Figure 7. The underlying grid and Piet Mondrian’s painting Composition With Yellow, Blue, and Red 1937–42. Copyright 2013 Mondrian/Holtzman Trust c/o HCR International USA.

extends from each station location on the abstract map to its actual geographic location. In the central area, the arrows point in, indicating expansion of the abstract map. (See Jenny, 2006, for a discussion of the approach and recent deformation maps of the Diagram.)

Another configuration technique found in the Diagram is the use of an underlying grid to support the vertical, horizontal, and diagonal line layout (Figure 7, next page). In some areas, the vertical and horizontal grid units are equalsided, but on the whole, the grid is rectilinear. The result is a “relaxed grid” (Alexander, 2002a, chap. 5) that has a certain rhythm and charm – somewhat similar to the grid used by modern artists (e.g., Piet Mondrian’s painting Composition With Yellow, Blue, and Red, 1937–42.

The same local symmetry, strong center, dynamic tension, deformation of the map, underlying grid, and the specific solutions to the station complexes were all present in the new designs developed after Beck’s 1959 departure. Although London Transport claimed, during the ensuing legal dispute, that these new designs were “worked out afresh within the framework of certain traditional practices associated with London Transport design,” it is quite clear who was responsible for these “traditional practices.” But because London

Transport held the legal ownership to Beck’s design, Beck’s courtroom battle with the conglomerate was futile. Oddly enough, the essence of his grievance was not so much about ownership per se as it was about the “privilege” of being commissioned for future work, or even just being privy to new designs (Garland, 1994, pp. 57–58).

Advanced Marketing During the first year of the dispute (1959–1960), Beck was under the impression that he might be called back. In an attempt to show his exceptional skills, or perhaps as a way of funneling his frustration, he came up with yet another configuration technique that was not only clever but also visionary in the extent to which it catered to the viewer’s evolving needs. In the late 1950s, work began on digging a new Tube line, which was to cross the city from southwest to northeast.

In anticipation, Beck took his published Diagram of 1959 and revised it such that the new Victoria Line would be the only full diagonal in the Diagram (see Figure 8 next page). Even though he colored the line a muted pale pink, it contrasted well with all the other lines, almost in an eerie relief.

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A Tale of Two Maps: Analysis of the London Underground “Diagram”

Figure 8. The network with the new Victoria Line as submitted to London Transport (circa 1961). Adapted from Mr. Beck’s Underground Map (p. 54), by K. Garland, 1994, Harrow Weald, UK: Capital Transport. Copyright 1994 by Capital Transport. Reproduced with permission.

in more than 30 years. Beck’s strategy was first to publish a new Diagram with all the adjustments necessary for including the Victoria Line but without showing the line itself. After the line was inaugurated, inserting it into the Diagram would require only minor changes to the respective interchange stations. And because the overall pattern of the Diagram would therefore not change, the public would have an easier time understanding how the new line fit into the network.

What is remarkable in this “promotion” strategy is the extreme sensitivity Beck showed with regard to the needs of users, not only in making sense of a complex network but also in supporting their needs over time.

Despite the fact that he was in the heat of the battle with London Transport, Beck submitted the revised Diagram to the agency in 1961. It was returned to him – without even a single comment. In 1964, he made another attempt to work on this promotional idea, based on a newer version of the Diagram developed by London Transport (Paul Garbutt, lead designer). The resulting Diagram is considered Beck’s best and most sophisticated ever (Garland, 1994, p. 60), yet it never saw the light of day. London Transport’s managers were

not prepared to receive any input from Beck; there was too much corporate pride riding on the Diagram.

In 1965, facing the reality of his limited financial resources for a prolonged legal battle against London Transport, and with his wife suffering from depression as a result of the legal dispute, Beck gave up the struggle. He died in 1974, bitter and betrayed by the very organization he had helped, so admirably, to promote.

Conclusion In 1931, with that touch of ingenious insight and a year’s worth of detailed work, Henry Beck created what is considered by many to be the most celebrated graphic design of the 20th century. The Diagram was initially rejected by London Transport managers for being “too revolutionary,” only to be accepted a year later. In the years since, this diagrammatic design approach became not only an essential guide to London but also a template for transport maps the world over (Rawsthorn, 2012). By some accounts, Beck, who was not commissioned to develop the initial design and worked on it in his spare time, was never actually paid for the job; others

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A Tale of Two Maps: Analysis of the London Underground “Diagram�

Figure 9. The current (2012) Diagram. Copyright 2012 by the Transport for London Company. Reprinted with permission.

have reported that the price was 5 or 10 guineas. Regardless, it was a meager tribute given that the Diagram is reproduced more than 60 million times each year by companies other than London Transport.

Design-wise, Beck’s innovative approach also paid well for London Transport. It turned out to be flexible enough to effectively accommodate all the new stations and lines that have been added in the 80 years since 1933 (Figure 9); it also supports the prototype of a future Underground network, including several lines to be added in decades to come.

Toward Formal Design Principles At the heart of the transformation from the concrete to the diagrammatic design lie several abstraction, integration, and configuration principles. In the London Underground map, for example, the basic city structure is preserved with respect to geographical landmarks (e.g., the River Thames) and main underground stations. This structure is preserved so as to facilitate ease of orientation and stress-free navigation by users of the network. On the other hand, there is no strict insistence on relative location - that is, north-south and eastwest - between remote and unrelated stations. However, it can be noted that relative line orientation between stations on the same line is preserved (north-south vs. east-west), and all lines are rectified to horizontal, vertical, or diagonal

orientation (such that between each station pair, one of these three possibilities is selected). Finally, note that the number of orientation changes of the lines is kept to a minimum.

These observations can be formalized as a set of mathematical constraints to be satisfied by any formal (e.g., algorithmically aided) design method: 1. A fundamental skeletal grid that consists of main stations and landmarks (e.g., the River Thames) must be selected as a foundation for the diagram to retain the essential structure of the concrete system.

2. The relative orientation of all other stations with respect to these fundamental grid points must be maintained.

3. The relative locations (west, east, north, south) of stations connected by a line must be consistent.

4. Line orientations in the abstracted map must be kept to a small set. In the London map, for example, there are three (horizontal, vertical, and diagonal).

5. The number of line orientation changes must be kept to a minimum.

An important goal of our work on the organization of information is the development of a formal mathematical methodology that can generate a set of reasonable starting

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A Tale of Two Maps: Analysis of the London Underground “Diagram”

solutions that satisfy the aforementioned design constraints.

One possible approach is a linear programming solution.

The second challenge is to come up with a formal solution for integration. In many respects, this problem is more artistic and less formally tractable than the abstraction and configuration problems. There are two aspects to integration: The first concerns the multiplicity of features of and interrelations among the elements to be integrated; the second is the arrangement of these interrelations so as to achieve a visually coherent and effective set (note the different solutions proposed by Beck for the Aldgate triangle in Figure 7).

A possible clue to developing a proper representation and computation of the integration problem is the observation that different elements (e.g., stations) have one or more properties of a specified list (e.g., line connectivity, pedestrian passages, geographic orientation, proximity) and thus possess pairwise interrelation, of varying degree, with all other elements. Accordingly, stations can be clustered with other stations in sets based on shared properties and the degree of affinity between each station pair. As such, each station may belong to a number of clusters that represent different sets of properties and relations. These clusters form the basis for generating the set of possible integration solutions.

One possible formal approach to the representation of relations and creating appropriate clusters is graph theory. (See Shmueli et al., in press, for the application of the approach to automotive systems.)

Beyond the design of transportation maps and diagrams for tourist maps and museums, what is the utility of such principles and formal techniques? Two main avenues come to mind: First, given that any human interaction with technology can be represented as a network (e.g., automotive climate control system, aircraft fuel system, medical devices), it is possible to apply these principles and techniques to the design of their (always abstract) interfaces. Second, there is a developing trend toward dynamic and adaptive interfaces that are tailored to users’ specific needs and that reconfigure themselves accordingly. Such reconfigurable interfaces require computational methods and suitable algorithms for their generation.

References Alexander, C., Ishikawa, S., & Silverstein, M. (1977). A pattern language. New York, NY: Oxford University Press.

Alexander, C. (2002a). The phenomenon of life. Berkeley, CA: Center for Environmental Structure.

Alexander, C. (2002b). The process of creating life. Berkeley, CA: Center for Environmental Structure.

Barshi, I., Degani, A., Iverson, D., & Lu, P. J. (2012). Using medieval architecture as inspiration for display design: Parameter interrelationships and organizational structure. In Proceedings of the Human Factors and Ergonomics Society 56th Annual Meeting (pp. 1799–1803). Santa Monica, CA: Human Factors and Ergonomics Society.

Bennett, K., & Flach, J. (2011). Display and interface design: Subtle science, exact art. Boca Raton, FL: CRC Press.

Degani, A., Barshi, I., & Shafto, M. (in press). Information Organization in the Airline Cockpit: Lessons from Flight 236. Journal of Cognitive Engineering and Decision-Making. Santa Monica, CA: Human Factors and Ergonomics Society.

Degani, A., Jorgensen, C., Shafto, M., & Olson, L. (2009). On organization of information: Approach and early work (NASA Technical Memorandum No. 215368). Moffett Field, CA: NASA Ames.

Garland, K. (1994). Mr. Beck’s Underground map. Harrow Weald, UK: Capital Transport.

Jenny B. (2006). Geometric distortion of schematic network maps. Bulletin of the Society of Cartographers, 40, 15–18.

Jung, C. G. (1955/1972). Mandala symbolism. Princeton, NJ: Princeton University Press.

Leboff, D., & Demuth, T. (1999). No need to ask: Early maps of the London Underground railways. Harrow Weald, UK: Capital Transport.

Monmonier, M. (1996). How to lie with maps. Chicago, IL: University of Chicago Press, Rawsthorn, A. (2012, August 5). The subway map that rattled New Yorkers.

New York Times. http://www.nytimes.com/2012/08/06/arts/design/ the-subway-map-that-rattled-new-yorkers.html?_r=0 Shmueli, Y., Degani, A., Zelman, A., Asherov, R., Zande, D., Weiss, J., & Bernard, A. (in press). Toward a Formal Approach to Information Integration: Evaluation of an Automotive Instrument Display. Proceedings of the 2013 International Annual Meeting of the Human Factors and Ergonomics Society Woodcock, J., & Davies, J. (1996). Using Z: Specification, refinement, and proof. London, UK: Prentice Hall.

Asaf Degani is a research scientist at GM’s Advanced Technical Center, Israel. His current research is on formal methods of information organization for the design of automotive systems.

Prior to joining GM, he worked for NASA Ames for 20 years, where he conducted research in aviation safety, cockpit design, and human-automation interaction.

He received his PhD in industrial and systems engineering from Georgia Institute of Technology, Atlanta.

Copyright 2013 by Human Factors and Ergonomics Society. All rights reserved.

DOI: 10.1177/1064804613489125

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