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.

 
 
 
 

Urgently needed: Timely, more detailed standardized data on US evictions

Graffiti asking for rent forgiveness is seen on a wall on La Brea Ave amid the Covid-19 pandemic in Los Angeles, California. (Valerie Macon/AFP via Getty Images)

Last week the Eviction Lab, a team of eviction and housing policy researchers at Princeton University, released a new dashboard that provides timely, city-level US eviction data for use in monitoring eviction spikes and other trends as Covid restrictions ease. 

In 2018, Eviction Lab released the first national database of evictions in the US. The nationwide data are granular, going down to the level of a few city blocks in some places, but lagged by several years, so their use is more geared toward understanding the scope of the problem across the US, rather than making timely decisions to help city residents now. 

Eviction Lab’s new Eviction Tracking System, however, provides weekly updates on evictions by city and compares them to baseline data from past years. The researchers hope that the timeliness of this new data will allow for quicker action in the event that the US begins to see a wave of evictions once Covid eviction moratoriums are phased out.

But, due to a lack of standardization in eviction filings across the US, the Eviction Tracking System is currently available for only 11 cities, leaving many more places facing a high risk of eviction spikes out of the loop.

Each city included in the Eviction Tracking System shows rolling weekly and monthly eviction filing counts. A percent change is calculated by comparing current eviction filings to baseline eviction filings for a quick look at whether a city might be experiencing an uptick.

Timely US eviction data for a handful of cities is now available from the Eviction Lab. (Courtesy Eviction Lab)

The tracking system also provides a more detailed report on each city’s Covid eviction moratorium efforts and more granular geographic and demographic information on the city’s evictions.

Click to the above image to see a city-level eviction map, in this case for Pittsburgh. (Courtesy Eviction Lab)

As part of their Covid Resource, the Eviction Lab together with Columbia Law School professor Emily Benfer also compiled a scorecard for each US state that ranks Covid-related tenant protection measures. A total of 15 of the 50 US states plus Washington DC received a score of zero because those states provided little if any protections.

CityMetric talked with Peter Hepburn, an assistant professor at Rutgers who just finished a two-year postdoc at the Eviction Lab, and Jeff Reichman, principal at the data science research firm January Advisors, about the struggles involved in collecting and analysing eviction data across the US.

Perhaps the most notable hurdle both researchers addressed is that there’s no standardized reporting of evictions across jurisdictions. Most evictions are reported to county-level governments, however what “reporting” means differs among and even within each county. 

In Texas, evictions go through the Justice of the Peace Courts. In Virginia they’re processed by General District Courts. Judges in Milwaukee are sealing more eviction case documents that come through their courtroom. In Austin, Pittsburgh and Richmond, eviction addresses aren’t available online but ZIP codes are. In Denver you have to pay about $7 to access a single eviction filing. In Alabama*, it’s $10 per eviction filing. 

Once the filings are acquired, the next barrier is normalizing them. While some jurisdictions share reporting systems, many have different fields and formats. Some are digital, but many are images of text or handwritten documents that require optical character recognition programs and natural language processors in order to translate them into data. That, or the filings would have to be processed by hand. 

“There's not enough interns in the world to do that work,” says Hepburn.


Aggregating data from all of these sources and normalizing them requires knowledge of the nuances in each jurisdiction. “It would be nice if, for every region, we were looking for the exact same things,” says Reichman. “Instead, depending on the vendor that they use, and depending on how the data is made available, it's a puzzle for each one.”

In December of 2019, US Senators Michael Bennet of Colorado and Rob Portman of Ohio introduced a bill that would set up state and local grants aimed at reducing low-income evictions. Included in the bill is a measure to enhance data collection. Hepburn is hopeful that the bill could one day mean an easier job for those trying to analyse eviction data.

That said, Hepburn and Reichman caution against the public release of granular eviction data. 

“In a lot of cases, what this gets used for is for tenant screening services,” says Hepburn. “There are companies that go and collect these data and make them available to landlords to try to check and see if their potential tenants have been previously evicted, or even just filed against for eviction, without any sort of judgement.”

According to research by Eviction Lab principal Matthew Desmond and Tracey Shollenberger, who is now vice president of science at Harvard’s Center for Policing Equity, residents who have been evicted or even just filed against for eviction often have a much harder time finding equal-quality housing in the future. That coupled with evidence that evictions affect minority populations at disproportionate rates can lead to widening racial and economic gaps in neighborhoods.

While opening up raw data on evictions to the public would not be the best option, making timely, granular data available to researchers and government officials can improve the system’s ability to respond to potential eviction crises.

Data on current and historical evictions can help city officials spot trends in who is getting evicted and who is doing the evicting. It can help inform new housing policy and reform old housing policies that may put more vulnerable citizens at undue risk.

Hepburn says that the Eviction Lab is currently working, in part with the ACLU, on research that shows the extent to which Black renters are disproportionately affected by the eviction crisis.

More broadly, says Hepburn, better data can help provide some oversight for a system which is largely unregulated.

“It's the Wild West, right? There's no right to representation. Defendants have no right to counsel. They're on their own here,” says Hepburn. “I mean, this is people losing their homes, and they're being processed in bulk very quickly by the system that has very little oversight, and that we know very little about.”

A 2018 report by the Philadelphia Mayor’s Taskforce on Eviction Prevention and Response found that of Philadelphia’s 22,500 eviction cases in 2016, tenants had legal representation in only 9% of them.

Included in Hepburn’s eviction data wishlist is an additional ask, something that is rarely included in any of the filings that the Eviction Lab and January Advisors have been poring over for years. He wants to know the relationship between money owed and monthly rent.

“At the individual level, if you were found to owe $1,500, was that on an apartment that's $1,500 a month? Or was it an apartment that's $500 a month? Because that makes a big difference in the story you're telling about the nature of the crisis, right? If you're letting somebody get three months behind that's different than evicting them immediately once they fall behind,” Hepburn says.

Now that the Eviction Tracking System has been out for a week, Hepburn says one of the next steps is to start reaching out to state and local governments to see if they can garner interest in the project. While he’s not ready to name any names just yet, he says that they’re already involved in talks with some interested parties.

*Correction: This story initially misidentified a jurisdiction that charges $10 to access an eviction filing. It is the state of Alabama, not the city of Atlanta. Also, at the time of publication, Peter Hepburn was an assistant professor at Rutgers, not an associate professor.

Alexandra Kanik is a data reporter at CityMetric.