How many colours would you need to make London’s bus network more comprehensible?

Any colour you want as long as its red. Image: Getty.

Looking at Transport for London’s colour-coded bus trial in Barkingside, CityMetric editor Jonn Elledge found an interesting problem:

Even thinking about the maths does my head in – but it seems unlikely to me that every bus in London can be given a colour different from that of every bus it ever shares a stop with. At some bus stops, there’ll be two buses in violet.

So let’s have a go at this: given the current bus routes in London, how many colours would you need to so that no bus stop has two buses using the same colour?

TfL have their bus stop locations and routes available as open data so we can quickly get a feel for how hard a problem is actually is. The way I processed the file I ended up with 20,028 bus stops and 729 routes (we can probably have arguments about exact numbers, but go with me). A lot of those bus stops serve exactly the same routes as others – so there are only 4,129 unique nodes in this problem. Which is still lots, but feels more manageable.

While there probably an elegant mathematical approach, the boring brute force technique goes like this. Starting out with all bus routes sharing a single colour (let’s say blue), you get the computer to go through every bus stop and change routes to other colours to make sure that bus stop has only unique colours. You then repeat this until all bus stops have no duplicate colours.

You get different results for this depending what order you tackle the bus stops, so you run it with a few different orders to get a feel of about how many colours are needed. Running the program 1,000 times, the lowest number I get using this technique is 44. Lower numbers are probably possible through trying many more orders, but let’s say for the moment this is roughly right – you’d need 44 colours to apply this approach strictly to the entire London bus system. This is really too many colours to be able to usefully distinguish lines, so is probably a no-go.

We get more manageable numbers if we try a less strict version of the rule. If we let bus stops served by five or more routes have two routes of the same colour, the total number of colours required drops to 14. This is approaching a workable colour scheme in terms of actually being able to distinguish between all varieties.

When your number is up

But let’s move on from colours and think about what TfL is actually trying to do here: it wants to make it easier for people who don’t currently use buses to use buses.

It’s worth thinking about where bus route numbers currently come from:

When we introduce a new route – or make alterations to an existing route by splitting it – the last digit or digits of the historic ‘parent’ route are used wherever possible, so that passengers might associate the incoming route with its predecessor. This was the case in 2003, for instance, when route 414 was chosen as the number for the new route between Maida Hill and Putney Bridge, which was intended to augment route historic route 14 south of Hyde Park Corner.

In other words, bus routes numbers are path dependent on old naming decisions because of the desire to keep existing users happy. While this is probably a good idea, it can also end up in results that are very un-good for new users.

So if you ignored the past and the need to keep the millions of current users not confused, what could do if you just scrapped all the current route numbers and started from scratch? Specifically let’s look at two problems:

  • Ambiguous bus routes at the same stop that appear similar;

  • Hard to remember bus numbers.

If you don’t see why these things are problems, imagine yourself as a user for whom the concept of numbers is a bit fuzzier: for instance, dyslexic users for whom the number rearrange (where 365 and 635 might be similar), or those for whom the numbers are literally fuzzy because they’re less able to read the signs.


There are two key areas of ambiguity: digits that are visually similar to each other (66 and 68) and route numbers that are conceptually similar like 114 and 14.

For real world examples of conceptually confusing bus stops, there are 1,601 stops served by routes whose numbers wholly contain the number of another route at the same bus stop. While this is sometimes suggestive of similarity of route, in many instances it isn’t. If you’re at Church Lane the 71 and 671 share 88 per cent of stops in common – but if you’re at Southall Broadway, the 95 and 195 share just 0.1 per cent of their stops. Looking at all the stops with this problem, the average similarity is only 38 per cent.

As most journeys are short, differences at the far end of the route are probably not a problem for most users – but the point is, that vague, warm feeling that similar number routes at the same location should be similar is not backed up by the data.

There are also 205 stops that have routes which are anagrams of each other. The St Nicholas Center has the 407 and the 470, at Brooke Road you have the 76 and 67, and Lytton Grove has the 39 and the 93. This isn’t many in the grand scheme of things – but it’s not ideal.

While we’re thinking about which numbers are nicer than other, let’s look at research which numbers are easier to remember correctly than others. Milikowski & Elshout found that:

The order of memorability was

(1) Single digit numbers;

(2) Teen numbers (10-19);

(3) Doubled numbers (e.g. 44, 77, 22);

(4) Large tabled numbers (numbers which factor and therefore appear in the multiplication tables, such as 49, 36, 60, 84, 27); and

(5) Other numbers that do not fall into any of these categories.

While memorability for Single digit numbers was above 80 percent, that for Other numbers (no subcategory) was only around 40 percent.

This should inform our thinking about route numbers. The first thing our colour system lets you do is dump bus numbers above 100 and use colours as a replacement for the first digit. This immediately makes numbers easier to remember because we’re reducing the number of concepts you need to remember. Route 127 requires you to remember three things (one two seven) while Blue-27 requires you to remember two (Blue twenty-seven). This is more true with smaller numbers, but every little helps.

The next thing we need to do is jettison every number that is a reverse of another (we don’t want both 46 and 64). This gets rid of most numbers above fifty (while retaining doubles). The end result is each colour can now be followed by 62 numbers – which means 62 bus routes.

Ideally you’d also reduce ambiguous symbols such as (1 and 7) or (6 and 8) – but this really cuts down the number of usable numbers. Instead what we’ll do try and make sure ambiguous numbers like this do not appear at the same stop.

Seeing clearly

So here are our new constraints:

  • A colour can only have 62 routes;

  • There are 15 colours (up from 14, because the original solution required some colours to have more than 62 routes);

  • Bus stops with four or fewer buses can’t have multiple routes with the same colour, stops with more can have two;

  • One bus stop cannot have routes of different colours with the same number. You also can’t have both 21 and 27, or 46 and 48.

Is such an arrangement possible? It turns out it is.

To solve this one you randomise which routes get which numbers and score them according to how well they pass the above. Then you create random variations on the best performing plan, and so on, until it narrows in on a version that passes all the rules. This returned a viable arrangement of route colours and names after a few hours (and 161,663 attempts).

Can something like this be done in reality? Confusing all current users seems a bad idea – but maybe this kind of approach should affect how new bus routes are named. Rather than blindly following the history of a route, select rules you want to be true of your naming scheme (they might be different from mine) and get a computer to suggest the minimally confusing approach. It turns out it doesn’t take long to get answers to quite fiddly problems.

But the real point here is I don’t want to wear my glasses to wait for a bus, and changing the naming convention for every single bus route in London is a proportionate response to this problem.

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Owning public space is expensive. So why do developers want to do it?

Granary Yard, London. Image: Getty.

A great deal has been written about privately owned public space, or POPS. A Guardian investigation earlier this year revealed the proliferation of “pseudo-public spaces”. Tales of people being watched, removed from or told off in POPS have spread online. Activists have taken to monitoring POPS, and politicians on both sides of the pond are calling for reforms in how they are run.

Local authorities’ motives for selling off public spaces are normally simple: getting companies to buy and maintain public space saves precious public pounds. Less straightforward and often overlooked in this debate is why – given the maintenance costs, public safety concerns and increasingly unflattering media attention – developers would actually want to own public space in the first place.

To answer that question it’s important to note that POPS can’t be viewed as isolated places, like parks or other public spaces might be. For the companies that own them, public spaces are bound up in the business that takes place inside their private buildings; POPS are tools that allow them, in one way or another, to boost profits.

Trade-offs

In some cities, such as Hong Kong and New York, ownership of public space is a trade-off for the right to bend the rules in planning and zoning. In 1961 New York introduced a policy that came to be known as ‘incentive zoning’. Developers who took on the provision of some public space could build wider, taller buildings, ignoring restrictions that had previously required staggered vertical growth to let sunlight and air into streets.

Since then, the city has allowed developers to build 20m square feet of private space in exchange for 80 acres of POPS, or 525 individual spaces, according to watchdog Advocates for Privately Owned Public Space (APOPS).

Several of those spaces lie in Trump Tower. Before the King of the Deal began construction on his new headquarters in 1979, he secured a pretty good deal with the city: Trump Tower would provide two atriums, two gardens, some restrooms and some benches for public use; in exchange 20 floors could be added to the top of the skyscraper. That’s quite a lot of condos.

Shockingly, the current president has not always kept up his end of the bargain and has been fined multiple times for dissuading members of the public from using POPS by doing things like placing flower pots on top of benches – violating a 1975 rule which said that companies had to provide amenities that actually make public spaces useable. The incident might suggest the failure of the ‘honour system’ under which POPS operate day-to-day. Once developers have secured their extra square footage, they might be tempted to undermine, subtly, the ‘public’ nature of their public spaces.

But what about where there aren’t necessarily planning benefits to providing public space? Why would companies go to the trouble of managing spaces that the council would otherwise take care of?


Attracting the ‘right sort’

Granary Square, part of the £5bn redevelopment of London’s Kings Cross, has been open since 2012. It is one of Europe’s largest privately-owned public spaces and has become a focal point for concerns over corporate control of public space. Yet developers of the neighbouring Coal Drop Yards site, due to open in October 2018, are also making their “dynamic new public space” a key point in marketing.

Cushman Wakefield, the real estate company in charge of Coal Drops Yard, says that the vision of the developers, Argent, has been to “retain the historical architecture to create a dramatic environment that will attract visitors to the 100,000 square feet of boutiques”. The key word here is “attract”. By designing and managing POPS, developers can attract the consumers who are essential to the success of their sites and who might be put off by a grubby council-managed square – or by a sterile shopping mall door.

A 2011 London Assembly Report found that the expansion of Canary Wharf in the 1990s was a turning point for developers who now “assume that they themselves will take ownership of an open space, with absolute control, in order to protect the value of the development as a whole”. In many ways this is a win-win situation; who doesn’t appreciate a nice water feature or shrub or whatever else big developer money can buy?

The caveat is, as academic Tridib Banerjee pointed out back in 2001: “The public is welcome as long as they are patrons of shops and restaurants, office workers, or clients of businesses located on the premises. But access to and use of the space is only a privilege and not a right” – hence the stories of security guards removing protesters or homeless people who threaten the aspirational appeal of places like Granary Square.

In the US, developers have taken this kind of space-curation even further, using public spaces as part of their formula for attracting the right kind of worker, as well as consumer, for nearby businesses. In Cincinnati, developer 3CDC transformed the notoriously crime-ridden Over-The-Rhine (OTR) neighbourhood into a young professional paradise. Pouring $47m into an initial make-over in 2010, 3CDC beautified parks and public space as well as private buildings.

To do so, the firm received $50 million  in funding from corporations like Procter and Gamble, whose Cincinnati headquarters sits to the South-West of OTR. This kind of hyper-gentrification has profoundly change the demographics of the neighbourhood – to the anger of many long-term residents – attracting, essentially, the kind of people who work at Procter and Gamble.

Elsewhere, in cities like Alpharetta, Georgia, 3CDC have taken their public space management even further, running events and entertainment designed to attract productive young people to otherwise dull neighbourhoods.

Data pools

The proposed partnership between the city of Toronto and Sidewalk Labs (owned by Google’s parent company Alphabet) has highlighted another motive for companies to own public space: the most modern of all resources, data.

Data collection is at the heart of the ‘smart city’ utopia: the idea that by turning public spaces and the people into them into a vast data pool, tech companies can find ways to improve transport, the environment and urban quality of life. If approved next year, Sidewalk would take over the mostly derelict east waterfront area, developing public and private space filled with sensors.

 Of course, this isn’t altruism. The Globe and Mail describe Sidewalk’s desired role as “the private garbage collectors of data”. It’s an apt phrase that reflects the merging of public service and private opportunity in Toronto’s future public space.

The data that Sidewalk could collect in Toronto would be used by Google in its commercial projects. Indeed, they’ve already done so in New York’s LinkNYC and London’s LinkUK. Kiosks installed around the cities provide the public with wifi and charging points, whilst monitoring traffic and pedestrians and generating data to feed into Google Maps.

The subway station at Hudson Yards, New York City. Image: Getty.

This is all pretty anodyne stuff. Data on how we move around public spaces is probably a small price to pay for more efficient transport information, and of course Sidewalk don’t own the areas around their Link Kiosks. But elsewhere companies’ plans to collect data in their POPS have sparked controversy. In New York’s Hudson Yards development – which Sidewalk also has a stake in – ambiguity over how visitors and residents can opt out of sharing their data when in its public square, have raised concerns over privacy.

In Toronto, Sidewalk have already offered to share their data with the city. However, Martin Kenney, researcher at the University of California at Davis and co-author of 2016’s ‘The Rise of the Platform Economy’, has warned that the potential value of a tech company collecting a community’s data should not be underestimated. “What’s really important is the deals Toronto cuts with Sidewalk may set terms and conditions for the rest of the world," he said after the announcement in October.

The project could crystallise all three motives behind the ownership of POPS. Alongside data collection, Sidewalk will likely have some leeway over planning regulations and will certainly tailor its public spaces to its ideal workers and consumers – Google have already announced that it would move its Canadian headquarters, from their current location in Downton Toronto, into the first pilot phase of the development.

Even if the Sidewalks Lab project never happens, the motives behind companies’ ownership of POPS tell us that cities’ public realms are of increasing interest to private hands.

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