redistorting maps: the virtue of cartograms

M. V. Jantzen has designed a fun tool that let's you rearrange a subway map to show actual travel times from where you are.  It's featured today at Greater Greater Washington.  Here's Washington DC Metro viewed from Ballston station in Virginia:


Jantzen calls this a "distortion," and with that I would disagree.  It's a redistortion, because as Mark Monmonier explains in his classic book, all useful maps are distorted.  Here's a whole page of Washington Metro maps, including the classic diagram


and a spatial one


Spatial maps are about spatial distance, and that's often, but not always, what matters.  The classic London Tube map is useful as a diagram, for example, but it can also undermine people's actual mental understanding of the geography of London.  

Source: Transport for London

Of the above image, Kerwin Datu writes: 

Bayswater and Queensway are 190 metres apart on the same street, Regent's Park and Great Portland Street 230 metres apart on the same street. But anyone going from Oxford Circus to either Bayswater or Great Portland Street would be persuaded that they had to take two trains to complete their trip.  … This is unacceptable in a low-carbon age, and with trains packed to the gills in peak hour … 

Back to the biggest picture point:

Maps that show one useful geography correctly seem so naturally authoritative that we can easily overvalue them when we really care about something else.  

Consider the way spatial geography is misused — by almost all media — to represent population.  If you think this is a useful map of the recent Iowa Republican caucuses …



… then you're misreading space as population.  The visual impression of dominating such a map arises from appealing to sparse rural voters who influence large spaces on the map.  Winning an election is something else.  The guy who won the orange counties did as well as the guy who won the purple ones, because the orange counties are where most people live.

(Updated) Back in the 2004 election, some smarter cartographers attempted maps (technically cartograms) in which each bit of area represented a fixed number of voters.  (Thanks to Niralisse for finding them for me!)  The US was reshaped into something looking like an angry cat wearing a corset, the mountain states reduced to almost nothing while the West and Northeast were enormous blobs.  


It took a while to get into, but it was an accurate visualization of what voters did.  It was a useful redistortion, arguably a net reduction in distortion, because when describing population-based data, a spatial map like the Iowa caucus map above is a distortion too.

Inevitably, as technology customizes everything around our individual narcissism perspectives and preferences, we'll get more used to "just for me" maps, maps that show how the universe really does revolve around ourselves.  These are crucial for their purpose.  I've especially praised this one, which shows where you can get to on transit, in a given time, from a point that you select.  

Ultimately, a clear vision of your city, your transit system, and your place in the world can only come from being able to move quickly between different kinds of maps, so that you're reminded at each moment that no map tells the whole story.  We must be able to redistort for ourselves, in real time.  If everyone had the tools to toggle quickly among different kinds of diagrams, they might even get over the notion that a spatial map tells you anything about an election.

12 Responses to redistorting maps: the virtue of cartograms

  1. Dan W. January 5, 2012 at 12:12 pm #

    A bit off topic, but if you are ever in London, please visit the London Transport Museum, which not only contains vehicles from the past, but has a gallery of London transit maps through the ages, going back to the horse and buggy days.

  2. Niralisse January 5, 2012 at 12:27 pm #

    Those size-by-statistic maps are called cartograms, and you can find a bevy of interesting ones here:

  3. Niralisse January 5, 2012 at 12:34 pm #

    Incidentally, I found the 2004 election ones you were looking for, along with a few other years here:

  4. Andrew January 5, 2012 at 12:59 pm #

    The problem of stations that are close together appearing far apart in London is inevitable when using a schematic map. A to-scale map would make the proximity of these stations obvious.
    The more serious problem with the London Underground map is that the standard map does not show the numerous commuter train services, which are often a faster/easier way to go certain places than the tube.

  5. Kenny Easwaran January 5, 2012 at 4:52 pm #

    Surely a schematic map of London doesn’t *have* to have this problem – if they did something like draw an extra line connecting two stations on different lines if they are under 250 meters apart on foot, that might be able to help people. It might increase visual clutter, but I think it would all depend on how common this situation is – if these pairs are the only two that are close enough to be redundant then it seems like it might be worthwhile, but if it happens all over then you might just expect users to watch for it independently rather than indicating it on the map.
    Also, the election maps have another potentially misleading feature – they don’t indicate how large the win was for any candidate. As I recall, the site with the cartogram for the 2000 and 2004 elections also has ones where each county is colored independently, and where the color is on a purple scale, so that you can tell that Cook County, IL was a much bigger win for Kerry than Orange County, CA was for Bush, despite having comparable population.

  6. Moaz Yusuf Ahmad January 5, 2012 at 8:38 pm #

    Kenny Easwaran is correct. It would be logical to add some kind of indicator to connect stations that are physically close to each other like the ones described.
    It is even more logical when you consider that Transport for London is also working on the Legible London project with the goal of helping Londoners walk.
    I suggest a small grey line linking the stations, with the legend saying “walking connection” or “street-level connection”.
    Otherwise, use the existing interchange design (shown at Paddington, Euston, Baker Street and Edgeware Road) with dashed lines instead of complete lines.
    Cheers, Moaz

  7. Brent January 5, 2012 at 9:02 pm #

    Something that I find useful to circumvent the problem of area vs. population is to use a dot-density map. Taking this back to transit, I find dot-density maps to be useful to show modal split geographically… say, one red dot for every 20 transit commuters, one blue dot for every 20 auto commuters, one green dot for every commuter rail commuters. I find this much more useful and descriptive than the usual way of shading the entire zone area based on proportion.

  8. Eric O January 6, 2012 at 5:15 am #

    Good point about the need to reconfigure maps on the fly. Putting time on the map, the Walk Score map communicates effectively the essential thing we care about the transit product, but the Metro distortion diagram gives us the narrative: the lines and connections by travel time. So at some level, you always have to access both information sets.
    When you toggle between conceptual frameworks, your own well-worn one and an analytic deconstruction (such as the Metro distortion diagram), you often find the kinks in your own personal framework. And that can be liberating.
    The narrative alone is not liberating. As humans, we still need handles to mesh such information to our personal image of the city, which are held together in our brains by the “Kevin Lynch five” (paths, edges, nodes, districts, landmarks). Transit maps tend to underplay the importance of this need (with the exception of water bodies – unfortunately, some cities don’t have these features). Zany tourist maps understand this need better, though these tend to be limited to walking districts. The narcissism of transit maps is that they conflate destination with station. Thankfully, stations and stops are not usually our destinations in the city, and for that reason we still need to see the National Mall on the map.
    Thus, a great base to adapt, methinks, is the Walk Score map. Note that the useful time information is a representational layer on a rather richly depicted map, which, with the advent of Google Maps, will possibly get our mental, travel and streetview frameworks better enmeshed with geographic accuracy. Note that implicitly the Kevin Lynch 5 are even being communicated with the Walk Score shapes on SF’s literal topography (the ridge geography), basically reinforcing our conceptualization of the city.

  9. GD January 6, 2012 at 5:44 am #

    call me elitist, but the problem starts with a lack of a larger public understanding of what a “model” (and every map is a model) is.
    When a professor in an advanced linguistics lecture used the tube map to explain the advantages and problems, and more importantly, the very basic idea of modelling anything, it was certainly an eye opener. But I was lucky and privileged to have that professor.
    So it’s not just the issue of having the right model for whatever it is you’re trying to understand, but also the knowledge that you’re modeling an aspect of reality – whether we’re talking about economics or something seemingly as simple as a tube map.
    Once you know that, however, you can gain valuable information from even a totally wrong (for your purpose) map. A friend and I successfully navigated Paris by car using only a mini-map of the metro that also showed a streetcar line. So once we hit the streetcar, following the tracks got us almost exactly where we wanted to go.

  10. Tom West January 6, 2012 at 6:27 am #

    With the Washington Metro map, it always takes me a moment to reliase the big blue line isn’t a subway line – it’s the river. I wish they’d downplay it.

  11. Tom West January 6, 2012 at 6:28 am #

    People who advocate geographically acurate transit maps because they’re “real” forget that no-one cares about distance with transit – they care about *time*.

  12. Steve Lax January 6, 2012 at 5:10 pm #

    @Tom West – When I use a transit map, I care about more than “time” by which I assume you mean travel time. I also care about frequency, even if in a table format. And, I care about distance from the transit stop to my final destination. (Can I walk the distance? Do I need to transfer to another rapid transit line or local bus?)
    Accordingly, when a transit map is not geographically accurate (and in many cases it would be difficult to read if it were), I need to rely on a geographically accurate street map as well, in almost all places.