Let us consider some of the special problems of mapping the Paris network diagrammatically. First, of course, there is the dense network of lines. Even in the 1950s there were 8 lines that crossed Paris (Lines 1, 3, 4, 5, 7, 8, 9, and 12) and another two that terminated in the centre (10 and 11). Creating enough space to name each station clearly and unambiguously has always been a challenge. Second, the lines of Paris do not so much twist and turn as knot themselves together. Lines cross each other, sprout stations, then change their mind and cross back again. For a diagrammatic map following Beck's 45-degrees rule, this gives a choice of either straight lines with lots of geographical distortion (don't forget that Londoners object to this happening in their own city), or preserving the relative spatial positions of stations but with lots of visually disturbing zig-zags. The third problem is that Paris is on a slant. Line 1 especially, following Champs Elysees, is at roughly 25 degrees to horizontal throughout most of its length. For a traditional diagrammatic map which angle should it be snapped to? Horizontal or 45 degrees? Things get difficult because the angle chosen then impinges on four other roughly-horizontally angled lines which are less steep: Lines 3, 8, and 9 are at roughly 12 degrees to horizontal, and although Line 10 is a little bit twisty, its overall trajectory is flat. Whatever angle Line 1 is going to be snapped to, this is going to result in at least one of the following problems: (1) uneven use of space as lines are compressed together or stretched apart more than in reality; (2) lots of kinks for trajectory correction to avoid (1); or (3) lots of geographical distortion.
In the 1950s, Beck was entering his 'straighten everything whatever the cost' phase of design (see Myth Number 6). Can you guess what happened in Paris? Lots and lots of geographical distortion.
It's always interesting to look at audience reaction to various maps posted on the internet. A lot of people are unsettled by geographical distortion to cities that they are familiar with. They can learn to live with this, but there is still a certain degree of discomfort. As long as the gain in clarity of the map makes up for the geographical discomfort, they are reasonably happy. A nice example of this is Heathrow Airport. The terminal loop (pre T5) is much easier to draw, and flows better, if T123 and T4 stations are shown incorrectly geographically. Quite a few people object to this when I design maps in this way. I point out that this information is irrelevant, that it is impossible to walk from T123 to T4 without getting killed or arrested (possibly both, but not necessarily in that order), but even when agreeing with this, people find the distortion irksome.
But show people a map of a city that they are unfamiliar with, and they are far less troubled by distortion. The map is evaluated on its own merits in terms of clarity, straight lines, and use of space. I wonder whether every city needs two maps: a tourist map with the clearest possible design, no matter how much geographical distortion there is, and a map for natives, which is less clear (more kinks etc.) but does a better job at preserving geography. To see what I mean, let's go back to Madrid:
Annie Mole's London Underground Blogspot (audience reaction here)
In general, as a result of experience of a city, people develop expertise in the form of what is called a mental model or a cognitive map. They have knowledge of where locations, landmarks, and waterways are, and roughly where to seek them out if they need to pinpoint them on a map. Henry Beck's designs before the Second World War were so successful because, on the whole, they did not conflict with people's mental models of London. In fact, the maps clarified and enhanced them. They organised London via the routes of its Underground lines so that its key thoroughfares were placed in a more orderly way, but without breaking their link with geography too much.
This takes us back to Paris, a very compact city, with the river taking a complicated but well-known route (with the labels left-bank and right-bank carrying important spatial connotations). Not only this, but the arrondissement system catalogues Paris into a small number of well-known zones, much more so than London's postal district system. What this all adds up to is that Paris natives will of course have a mental model of their city, and you conflict with this at your peril. So, let's take a look at Beck's 1951 map.
Of course, another of Beck's problems was that he was up against one of the best-designed geographical railway maps ever. Lagoutte's design was clear and elegant in a way that Stingemore's pre-Beck maps could not even approach. Street details were omitted, and even though there was little distortion, station names were clear and easy-to-read and lines were easy to follow.
Note the route taken by Line 1 (the middle one of three red lines), now look at what Beck did with it:
Paris has been tilted to its side and pushed to the right. Line 3 (in light blue, this parallels Line 1 to its north) has been tilted even more to match - remember that in reality it is less tilted, and is at about 12 degrees to horizontal. In fact, in London, the Central Line, although generally shown on maps as horizontal, also tilts by about the same amount, heading WSW rather than W. This gives us a handy way of showing Londoners just how disconcerting applying a tilt like this can be if you are familiar with a city:
Unfortunately, there were lots more problems with Beck's design. Tilting the city upsets the overall balance of the network, with vast empty spaces in some areas, and crushed together stations on others. Look at the horizontal stretches of line shown below, and compare the overall balance of the map with the official version. Also, Montparnasse Bienvenue caused Beck endless trouble (on a previous attempt he got it completely wrong). This time round, he missed out Vavin and Edgar Quinet stations (they go between Montparnasse and Raspail) with no obvious way of adding them.
So, overall then, Beck tilted the city of Paris to an extreme, and along with unbalanced spacing and non-preserved spatial relationships between nearby stations, his overall design distorted Paris enormously. Add to this some difficult-to-correct mistakes and it is not hard to imagine RATP officials having very little time for this map.But do the benefits of the design outweigh the problems? Would Parisians have got used to this distorting map? I suspect not. There are lots of nice straight lines, but the overall balance of the design is poor. Also, the only way in which the map can be used comfortably is without knowledge of Parisian geography. I know Paris fairly well, and trying to imagine myself using Beck's map, I kept finding myself looking for lines or stations where I expected them to be geographically, and failing to find them, or even misidentifying my target and going the wrong way (Paris has much less strong colour coding than London, and even today colour coding is poorly implemented). Distorting the streetmaps of Paris to match a Metro map is not an option, and needing two mental models of a city, one for reality, one for maps, adds to the mental work necessary. Overall then, Beck's map succeeds as an intellectual exercise (he was the first to do it, showing that it could be done) but not as an exercise in usability. You shouldn't push a diagrammatic map too far beyond people's mental models of their cities.