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.The Conversation

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

This article was originally published on The Conversation. Read the original article.


The smartphone app placing virtual statues of women on the map

A virtual Edith Wharton in Central Park, New York City. Image: The Whole Story Project.

If you’re a woman, then in order for you to be immortalised in stone, bronze or whatever once you’ve shuffled off this mortal coil, you should either have royal blood or be willing to be sculpted naked. That is the rule of thumb.

A statue that actually celebrates a woman’s achievements is a rare sight. Writing in the New Statesman last year, equality campaigner Caroline Criado-Perez found that out of 925 statues in Britain, as listed by the Public Monuments and Sculpture Association, only 158 are of solo women. Of these, 46 are of royalty, including 29 of Queen Victoria. Fourteen depict the Virgin Mary.

There are signs of change, albeit slow. The suffragist Millicent Fawcett is set to be honoured with a statue in Parliament Square, where currently all 11 of the statues are of men. (They include Nelson Mandela and a nine-foot Gandhi.) The monument is to be unveiled next year to celebrate the centenary of British women receiving the right to vote.

Elsewhere, the late comedian Victoria Wood is being honoured with a statue that’ll be erected in Bury, Greater Manchester. In the Moss Side area of the city, a statue of Emmeline Pankhurst will be unveiled in 2019. Unlike the Fawcett one, neither of these is expected to receive public money, relying on crowdfunding and other sources instead.

So how many more statues of women, regardless of how they’re funded, would we need to build in order to reduce the gender gap? Well, according to Jonathan Jones, art critic at the Guardian, the magic number is: zero.

Jones’s argument, back in March, was that building statues doesn’t advance feminism, but simply traps us in the past. He wrote:

Statues don’t hold public memory. They politely bury it. These well-meaning images melt into the background scenery of our lives.

Whether this is empirically true is questionable, but it’s true that we tend not to erect them as often as we used to anyway. This is partly because there is less space available for such monuments – a noticeable disadvantage cities of the present have compared to those of the past. In order to reduce the imbalance, statues of men would probably have to be removed; many would no doubt be okay with that, but it would mean erasing history.

One partial answer to the problem is augmented reality. It can’t close the gender gap, but it could shine a spotlight on it.

To that end, an advertising agency in New York launched an app at the beginning of May. The Whole Story allows users to place virtual statues of women on a map; other uses can then view and find out more about the individuals depicted at their real-world locations, using their smartphone cameras.

Currently, users have to upload their own virtual statues using 3D-modelling software. But going forward, the project aims for an open collaboration between designers, developers and organisations, which it hopes will lead to more people getting involved.

Contributions submitted so far include a few dozen in New York, several in Washington and one of Jane Austen in Hyde Park. There are others in Italy and the Czech Republic.

Okay, it’s an app created by a marketing firm, but there are legitimate arguments for it. First, the agency’s chief creative office has herself said that it’s important to address the gender imbalance in a visual way in order to inspire current and future generations: you can’t be what you can’t see, as the saying going.

Second, if the physical presence of statues really is diminishing and they don’t hold public memory, as Jones argues, then smartphones could bridge the gap. We live our lives through our devices, capturing, snapping and storing moments, only to forget about them but then return to and share them at a later date. These memories may melt away, but they’ll always be there, backed up to the cloud even. If smartphones can be used to capture and share the message that a gender imbalance exists then that’s arguably a positive thing.  

Third, with the success of Pokemon Go, augmented reality has shown that it can encourage us to explore public spaces and heighten our appreciation for architectural landmarks. It can also prove useful as a tool for learning about historical monuments.

Of course no app will replace statues altogether. But at the very least it could highlight the fact that women’s achievements are more than just sitting on a throne or giving birth to the son of God.

Rich McEachran tweets as @richmceachran.

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