# 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.

# Was the decline in Liverpool’s historic population really that unusual?

A view of Liverpool from Birkenhead. Image: Getty.

It is often reported that Liverpool’s population halved after the 1930s. But is this true? Or is it a myth?

Often, it’s simply assumed that it’s true. The end. Indeed, proud Londoner Lord Adonis – a leading proponent of the Liverpool-bypassing High Speed 2 railway, current chair of the National Infrastructure Commission, and generally a very influential person – stood on the stairs in Liverpool Town Hall in 2011 and said:

“The population of Liverpool has nearly halved in the last 50 years.”

This raises two questions. Firstly, did the population of the City of Liverpool really nearly halve in the 50 year period to 2011? That’s easy to check using this University of Portsmouth website – so I did just that (even though I knew he was wrong anyway). In 2011, the population of the City of Liverpool was 466,415. Fifty years earlier, in 1961, it was 737,637, which equates to a 37 per cent drop. Oops!

In fact, the City of Liverpool’s peak population was recorded in the 1931 Census as 846,302. Its lowest subsequent figure was recorded in the 2001 Census as 439,428 – which represents a 48 per cent decline from the peak population, over a 70 year period.

Compare this to the population figures for the similarly sized City of Manchester. Its peak population also recorded in the 1931 Census as 748,729, and its lowest subsequent figure was also recorded in the 2001 Census, as 392,830. This also represents a 48 per cent decline from the peak population, over the same 70 year period.

So, as can be seen here, Liverpool is not a special case at all. Which makes me wonder why it is often singled out or portrayed as exceptional in this regard, in the media and, indeed, by some badly briefed politicians. Even London has a similar story to tell, and it is told rather well in this recent article by a Londoner, for the Museum of London. (Editor’s note: It’s one of mine.)

This leads me onto the second question: where have all those people gone: London? The Moon? Mars?

Well, it turns out that the answer is bit boring and obvious actually: after World War 2, lots of people moved to the suburbs. You know: cars, commuter trains, slum clearance, the Blitz, all that stuff. In other words, Liverpool is just like many other places: after the war, this country experienced a depopulation bonanza.

So what form did this movement to the suburbs take, as far as Liverpool was concerned? Well, people moved and were moved to the suburbs of Greater Liverpool, in what are now the outer boroughs of the city region: Halton, Knowsley, St Helens, Sefton, Wirral. Others moved further, to Cheshire West & Chester, West Lancashire, Warrington, even nearby North Wales, as previously discussed here.

In common with many cities, indeed, Liverpool City Council actually built and owned large several ‘New Town’ council estates, to which they moved tens of thousands of people to from Liverpool’s inner districts: Winsford in Cheshire West (where comedian John Bishop grew up), Runcorn in Halton (where comedian John Bishop also grew up), Skelmersdale in West Lancashire, Kirkby in Knowsley. There is nothing unique or sinister here about Liverpool (apart from comedian John Bishop). This was common practice across the country – Indeed, it was central government policy – and resulted in about 160,000 people being ‘removed’ from the Liverpool local authority area.

Many other people also moved to the nearby suburbs of Greater Liverpool to private housing – another trend reflected across the country. It’s worth acknowledging, however, that cities across the world are subject to a level of ‘churn’ in population, whereby many people move out and many people move in, over time, too.

So how did those prominent images of derelict streets in the inner-city part of the City of Liverpool local authority area come about? For that, you have to blame the last Labour government’s over-zealous ‘Housing Market Renewal Initiative’ (HMRI) disaster – and the over enthusiastic participation of the then-Lib Dem controlled city council. On the promise of ‘free’ money from central government, the latter removed hundreds of people from their homes with a view to demolishing the Victorian terraces, and building new replacements. Many of these houses, in truth, were already fully modernised, owner-occupied houses within viable and longstanding communities, as can be seen here in Voelas Street, one of the famous Welsh Streets of Liverpool:

Voelas Street before HMRI implementation. Image: WelshStreets.co.uk.

The same picture after HMRI implementation Image: WelshStreets.co.uk.

Nonetheless: the council bought the houses and ‘tinned them up’ ready for demolition. Then the coalition Conservative/Lib Dem government, elected in 2010, pulled the plug on the scheme.

Fast forward to 2017 and many of the condemned houses have been renovated, in a process which is still ongoing. These are over-subscribed when they come to market, suggesting that the idea was never appropriate for Liverpool on that scale.

At any rate, it turns out that the Liverpool metropolitan population is pretty much the same as it was at its peak in 1931 (depending where the local borough boundaries are arbitrarily drawn). It just begs the question: why are well educated and supposedly clever people misrepresenting the Liverpool metropolis, in particular, in this way so often? Surely they aren’t stupid are they?

And why are some people so determined to always isolate the City of Liverpool from its hinterland, while London is always described in terms of its whole urban area? It just confuses and undermines what would otherwise often be worthwhile comparisons and discussions. Or, to put it another way: “never, ever, compare apples with larger urban zones”.

In a recent Channel 4 documentary, for example, the well-known and respected journalist Michael Burke directly compared the forecast population growths, by 2039, of the City of Liverpool single local authority area against that of the combined 33 local authority areas of Greater London: 42,722 versus 2.187,708. I mean, what bizarre point is such an inappropriate comparison even trying to make? It is like comparing the projected growth of a normal sized-person’s head with the projected growth of the whole of an obese person, over a protracted period.

Having said all that, there is an important sensible conversation to be had as to why the populations of the Greater Liverpool metropolis and others haven’t grown as fast as maybe should have been the case, whilst, in recent times, the Greater London population has been burgeoning. But constantly pitching it as some sort of rare local apocalypse helps no one.

Dave Mail has declared himself CityMetric’s Liverpool City Region correspondent. He will be updating us on the brave new world of Liverpool City Region, mostly monthly, in ‘E-mail from Liverpool City Region’ and he is on twitter @davemail2017.