# How can you escape from a maze – and what does that teach us about city planning?

“Sorry, we live here now”. Image: Getty.

Mazes are in vogue at the moment, from HBO’s Westworld, to the return of the British cult gameshow, The Crystal Maze. But mazes have been around for millennia and one of the most famous mazes, the Labyrinth home of the Minotaur, plays a starring role in Greek mythology.

Which begs the question: what is the difference between a maze and a labyrinth? Although considered synonymous by some, it is generally accepted that a labyrinth contains only one path, often spiralling around and folding back on itself, in ever-decreasing loops, whereas a maze contains branching paths, presenting the explorer with choices and the potential for getting very, very lost.

While designing a maze can be a rewarding human task, computer scientists and mathematicians have a love of maze-generating algorithms. The algorithms tend to fall into two principal types: ones which start with a single, bounded space and then sub-divide it with walls (and doors) to produce ever smaller sub-spaces; and others which start with with a world full of disconnected rooms and then demolish walls to create paths/routes between them.

### The great escape

There are techniques for escaping from mazes, but first you need to be sure what kind of maze it is. Most methods work for “simple” mazes, that is, ones with no sneaky short-cuts via bridges or “passage loops” – circular paths that lead back to where they started.

So, assuming it is a simple maze, the method that many people know is “wall-following”. Essentially, you place one hand on a wall of the maze (it doesn’t matter which hand as long as you are consistent) and then keep walking, maintaining contact between your hand and the wall. Eventually, you will get out. This is because if you imagine picking up the wall of a maze and stretching its perimeter to remove any corners, you will eventually form something circle-like, part of which must form part of the maze’s outer boundary. This method of escape may not work, however, if the start or finish locations are in the maze’s centre.

But some mazes are deliberately designed to frustrate, such as the Escot Gardens’ beech hedge maze in Devon, which contains no fewer than five bridges, and so far from “simple”.

Another method of maze escape, known as Trémaux’s algorithm, works in all cases.

Imagine that, like Hansel and Gretel in the fairy story, you are able to leave a trail of “breadcrumbs” behind you as you navigate your way through the maze and then remember these rules: if you arrive at a junction you have not previously encountered (there will be no crumbs already on the trail ahead), then randomly select a way to go. If that leads you to a junction where one path is new to you but the other is not, then select the unexplored path. And if choosing between a once or twice-used path, choose the path used once, then leave a new, second trail behind you. The cardinal rule is never, ever select a path already containing two trails. This method is guaranteed, eventually, to get you out of any maze.

### Everyday mazes

So how is any of this maze stuff useful? Well, from the perspective of architecture and urban design, we want to avoid accidentally creating mazes. Mazes are fun, but are not necessarily something we want in our everyday lives – or in our way when we just want to get to work.

In the 1980s, the architectural theorist, Bill Hillier, observed that many of the most socially problematic housing estates were those that appeared to be somewhat “maze-like” in their layout. This begged the theoretical question: how do we actually measure the “maze-iness” of a place?

Barnsbury, in London: extremely unmaze-like. Image: Google Maps.

To answer this, Hillier developed the measure of “intelligibility”, which is the relationship between what is immediately visible from a single location in a maze/housing estate/neighbourhood and how accessible that same place is from other locations in the area. The measure ranges from 0 to 1: environments that score highly (greater than 0.5) tend to be quite intelligible, easy to understand and navigate, and frequently desirable – for example Barnsbury, in London.

Conversely, places with a low intelligibility score tend to be confusing, hard to navigate and, ultimately, maze-like – London’s Barbican Estate, although architecturally lauded, is so confusing that visitors need to follow the yellow lines in order to find their way around.

It was this measure of intelligibility that we used to design the game levels in the recent SeaHeroQuest game, a game designed to measure people’s navigational skills in order to further dementia research.

We “reverse-engineered” intelligibility in order to produce game levels that were more, or less, maze-like, to ensure a range of challenges for the players. So the mathematics of maze design is just as applicable in modern, dementia-battling apps as it was in distant Greek mythology.

Ruth Dalton is professor of building usability and visualisation, and Nick Dalton a lecturer in computing and communications, at Northumbria University, Newcastle.

# “This is a civic pride for the digital age”: why we should why we should willingly let City Hall have our data

He was the future once: David Cameron discusses smart cities with Angela Merkel and a German technology executive. Image: Getty.

Victorian England. From the shadows of wealth grew poverty. Slums slumped against symbols of civic pride, cowering next to towering town halls funded through rich merchant princes, whose elitist rule was insufficient to deal with too many people in too few houses with too little infrastructure.

Enter municipality. With darkness came electric light; with disease came tunnels to disperse their cause; with time came reform, regulation and the rise of town planning.

It’s over a century since those places which first industrialised became those first urbanised; yet even the wealthiest cities in the world continue to struggle with the complexities of urbanisation. In London, ten thousand die each year from pollution; in New York, six times this amount reside in homeless shelters.On the rush-hour roads of Sydney, cars stand still, and in the ‘burbs or banlieues of Paris slums still stand.

An umbrella bought during a downpour costs more than one bough under blue sky – and the truth is that, for too, long city halls have failed to forecast and so incurred greater costs. It’s a reactive culture summed up by words first head in Jimmy Carter’s budget office: if it ain’t broke, don’t fix it. Disease before sewer, gridlock before investment, collapse before rebuild – visible fix over unseen prevention

But with the world’s urban population growing by 65m every year, this has to change: there is not enough resource to manage cities reactively. Enter technology and the move to smart cities.

From Barcelona to New YorkOxford to Amsterdam, Singapore to Seoul: billions of low-cost devices are being installed into everyday objects to send and receive data: street lights recording pollution, and bridges reporting performance; traffic lights that count, and whose analysis will be counted upon, to ease traffic congestion; health wristbands understanding our heart’s needs, shop ceilings noting our heart’s desires. A web of information woven into the very fabric of cities which, when added to data from sources like mobile phones, is providing a living-breathing picture of how we and our cities operate.

This data is no longer retrospective or historic but live and dynamic. It is of such quantity, and can be analysed at such granular detail, that it can provide certainty where once there was only supposition. It is build-up before the gridlock, illness before epidemic; the crack of an ageing bridge, the first signs of smog. It is diagnostic to preventative. Umbrella under blue sky.

Those promoting the “internet of things”, estimated to be worth \$11.1trn a year by 2025, will declare it a panacea – but it is not, at least not entirely. Sure, challenges regarding data quality, privacy, standardisation, and security will be overcome; 4G will become 5G will become 6G. Devices will communicate intelligently with each other – autonomous vehicle to autonomous vehicle, autonomous vehicle to bridge, drone to home. Data will become as fundamental to cities as infrastructure, and will be referred to as such.

Yet city halls in democracies, whilst infinitely better informed, will continue to make their decisions which are restricted by commercialism, framed by political ideology, and driven by short-term electoral or media pressures.

### People first

From the mid-sixties to the start of this century a UK television programme called Tomorrow’s World showcased future living. For every correct prediction (mobile phones) came countless incorrect ones: the floating-bicycle, say, or paper underwear. My point is that only a small part of understanding the future of cities is about understanding technology. The majority is about understanding people and society, the people from whom the very word “city” is derived: civitas, the collective of citizens.

Gutenberg did not change the world by inventing the printing press in the 13th century – but he did enable the world to change. The technology was the printing press, the outputs were books filled with knowledge, the outcomes were the actions of the many who used that knowledge. Technology is a tool, a process towards an outcome.

In much the same way, the Internet of Things will not change the world – but it will enable the world to change. Sensors are the technology, data the outputs, the analysis of this data and subsequent decisions, the outcome.

It is crucial to avoid the Tomorrow’s World approach. That is, racing to implement technology first without consideration of identified social, economic or environmental needs; introducing more complexity when most citizens seek simplicity. As the writer and urbanist Jane Jacobs once said:“First comes the image of what we want, then the machinery is adapted to turn out that image.”

Start with people. Form the image. Think of technology through the Greek origins of the word, techne and logos – a discourse about the way things are gained – and capitalise on collective intelligence to move towards that image.

Since cities first started to appear some millennia ago, they’ve provided incontrovertible evidence that the wisdom of crowds is far greater than the individual; that collective intelligence gained from that trinity of city institutions – citizen, government, industry – surpasses what can be achieved by any one in isolation. Where would Apple, Uber, or Google be without the government-backed inventions like the world-wide-web, touchscreen technology, WiFi or global positioning systems?

### A new civic pride

Of course, an app on a smart phone that can ask a thousand questions is meaningless if nobody feels motivated to answer. Increasing urbanisation brings increasing interdependency: lives intrinsically linked, services shared. The challenge for city halls is to turn the increase in what people have in common, into an increase in common purpose, through understanding the three benefits that motivate and lead to action.

Extrinsic benefits, of status and reward, caused merchant princes to fund city halls in Victorian England: such benefits today see the ambitious putting in extra hours. Intrinsic benefits, like competitiveness or fun, that once caused business tycoons to compete to build the tallest skyscrapers, now explain why “hackathons” and “city challenges” are such a success. Then there are the pro-social benefits of altruism or benevolence, that cause millions to volunteer their time to give back and feel part of something bigger than themselves.

These motivations are of greater significance, because there are no longer people with clipboards standing on street corners asking permission to collate our views on services: it is happening automatically through the Internet of Things. Our choices online, movements offline; the travel we take, the pollution we make; our actions and interactions. We are data.

City halls can take a click-box-small-print approach to this, like so many apps. But there is opportunity to do the opposite. They can promote the fact that citizens can knowingly provide their data towards making lives better; visualise and enable citizens to see and understand their input, alongside data provided by others.

They can incentivise interaction with data, so that entrepreneurs can work back from outcomes, solve challenges, and re-localise where appropriate (we should not need a multinational to get a taxi). They can be proudly open, enabling citizens, industry and government to receive pro-social benefit by contributing to something bigger than themselves: their life and the lives of others.

This is a civic pride for the digital age. Not just localism or patriotism based on geography but the strength of connection between people and their ability to direct and determine change through data. Not just pride in the buildings and infrastructure that form our physical world, but in the quality of data that will shape our future world and move us from a diagnostic to preventative society – umbrellas under blue sky.

We should take pride in technology, yes; but that should come second to the pride in those who, enabled by that technology, drive progress. Who, through the wisdom of crowds, form an image of the future and strengthen democracy by motivating society to move towards it. Who embrace openness and help overcome the challenges of urbanisation.

Kevin Keith is a writer, researcher, urbanist, and director of the southern hemisphere’s largest open data competition, GovHack. He tweets as@KevKeith.