Welcome back to Sunday reading. This week, let’s start with a new research paper on complexity. Oxford University researchers ask, “are big-city transportation systems too complex for human minds?

Many of us know the feeling of standing in front of a subway map in a strange city, baffled by the multi-coloured web staring back at us and seemingly unable to plot a route from point A to point B.

Now, a team of physicists and mathematicians has attempted to quantify this confusion and find out whether there is a point at which navigating a route through a complex urban transport system exceeds our cognitive limits.

After analysing the world’s 15 largest metropolitan transport networks, the researchers estimated that the information limit for planning a trip is around 8 bits. (A ‘bit’ is a binary digit — the most basic unit of information.)

Additionally, similar to the ‘Dunbar number’, which estimates a limit to the size of an individual’s friendship circle, this cognitive limit for transportation suggests that maps should not consist of more than 250 connection points to be easily readable.

Using journeys with exactly two connections as their basis (that is, visiting four stations in total), the researchers found that navigating transport networks in major cities — including London — can come perilously close to exceeding humans’ cognitive powers.

And when further interchanges or other modes of transport — such as buses or trams — are added to the mix, the complexity of networks can rise well above the 8-bit threshold. The researchers demonstrated this using the multimodal transportation networks from New York City, Tokyo, and Paris.

Humans deal poorly with complexity and counterintuitive results. That’s an important thing to keep in mind when designing and communicating urban policies.

However, technology can help people navigate complexity. I’ve found that Google Maps, online journey planners, and smartphone apps have made it much easier to use public transport when visiting new cities. But a reliance on GPS mapping can lead to some unintended consequences, as Greg Milner explores in this New York Times article:

Earlier this month, Noel Santillan, an American tourist in Iceland, directed the GPS unit in his rental car to guide him from Keflavik International Airport to a hotel in nearby Reykjavik. Many hours and more than 250 icy miles later, he pulled over in Siglufjordur, a fishing village on the outskirts of the Arctic Circle. Mr. Santillan, a 28-year-old retail marketer from New Jersey, became an unlikely celebrity after Icelandic news media trumpeted his accidental excursion.

Mr. Santillan shouldn’t be blamed for following directions. Siglufjordur has a road called Laugarvegur, the word Mr. Santillan — accurately copying the spelling from his hotel booking confirmation — entered in lieu of Laugavegur, a major thoroughfare in Reykjavik. The real mystery is why he persisted, ignoring road signs indicating that he was driving away from Iceland’s capital. According to this newspaper, Mr. Santillan apparently explained that he was very tired after his flight and had “put his faith in the GPS.”

[…] Could society’s embrace of GPS be eroding our cognitive maps? For Julia Frankenstein, a psychologist at the University of Freiburg’s Center for Cognitive Science, the danger of GPS is that “we are not forced to remember or process the information — as it is permanently ‘at hand,’ we need not think or decide for ourselves.” She has written that we “see the way from A to Z, but we don’t see the landmarks along the way.” In this sense, “developing a cognitive map from this reduced information is a bit like trying to get an entire musical piece from a few notes.”

And now, for a break from cognitive science, here’s an animated GIF of a bicycle-storage system in Japan. This certainly seems simple enough to use:

Complexity is not just an issue when getting around. It’s also a very serious issue for housing and urban planning policy. We saw that this week, with various people, including councillors, denying that enabling more housing would improve housing affordability.

As an economist, I cannot disagree strongly enough with this bizarre analysis. But it’s fair to say that the workings of housing markets are extremely complex and often counterintuitive. As Daniel Hertz at CityObservatory discusses, with reference to recent research, new dwellings tend to be more expensive than old ones (duh!) but they gradually “filter” down to the rest of the market:

But very little private housing in the United States was originally built for low-income people. Instead, homes built for the middle or even upper classes gradually became cheaper as they aged, as people with high purchasing power moved into trendier, more modern homes in “better” neighborhoods. As higher income households move on, the now somewhat older homes or apartments they formerly occupied are sold or rented to people with more modest incomes.

This process is called “filtering.” While the evidence that filtering is a real phenomenon has been around for a long time—the core of nearly every American city contains neighborhoods with once-luxurious homes now occupied by people of modest incomes—the first study to provide a rigorous measure of how it happens was published only in 2013. In it, Stuart Rosenthal of Syracuse University uses nearly 40 years of data from the American Housing Survey to figure out the average pace of filtering across the country, and what makes housing filter more quickly in some places than others.

Rosenthal uses the AHS to compare the incomes of people living in the same units of housing over time. He estimates that nationwide, housing “filters” by roughly 1.9 percent a year—meaning that a 50-year-old home is typically occupied by someone whose income is about 60 percent lower than that home’s first occupant.

Filtering is complex but very real. By contrast, some urban issues are pretty simple. Take, for example, the role of urban trees in maintaining environmental quality and amenity. In the News Tribune, a newspaper in Washington state, Rosemary Ponnekanti reports on “why cities need trees: the science behind a 30 percent canopy“:

Trees are vital in keeping a city’s air and water healthy for people.

The American Forests study, called “Calculating the Value of Nature,” analyzed the Tacoma-Everett-Redmond triangle using images from 1972 to 1996.

Dollar values were placed on the ability of trees to control stormwater flooding ($2.4 billion annually) and filter air pollution ($95 million annually.)

The loss, over that period, of 600,000 acres of highly canopied land meant a 35 percent increase in stormwater runoff, which affects salmon populations, pollution in Puget Sound, flooding on city streets, soil erosion and more.

“Each tree absorbs hundreds of gallons of water, filtering it through the root system so clean water goes back to the ground,” said Pierce Conservation District’s Melissa Buckingham.

And by filtering greenhouse gases such as carbon dioxide out of the atmosphere, trees contribute over time to cooling the air, as well as cooling it in real time with shade during summer.

According to California nonprofit Canopy.org, evaporation from one tree can produce the same cooling effect as 10 room-size air conditioners. That lowers the average summer temperature in highly canopied cities such as Palo Alto, California (which has 37.6 percent canopy), by up to 8 degrees compared with neighboring areas.

We like trees. But they’re not the only thing that can make or break a place that are sometimes poorly understood by policymakers. Take the case of traffic studies, which often focus predominantly on movement of vehicles and ignore potential impacts on non-motorised travellers, surrounding properties, and the public realm. In an interesting blog post, Slow Streets points out that things left unmeasured by traffic studies are often important for understanding the value of bike lanes:

Don’t ignore the public space outside of your business. It’s an asset that should be cultivated and leveraged. This asset is often overlooked by the business community since it’s not directly indoors. Currently, the sidewalks of Commercial Drive do not offer a secure and pleasant place to stay or linger. Slow Streets found that Commercial Drive is a rather uncomfortable place for walking: sound volumes from traffic registered at 76DB, the equivalent of standing 15m from a highway. We also observed the activities of over 1,000 people and found that there was an apprehension to linger and socialize with only 14% of people observed doing so

By inviting people to stay and linger on the sidewalks of Commercial Drive, businesses could see an increase in revenue. In short, traffic calming is good for business. The sidewalks and public space outside of your business are a critical asset that can serve as a magnet to attract people. A bike lane will encourage people to spend time on the sidewalks on Commercial Drive because the public space is more comfortable. Reductions in automobile speeds and volumes reduce the noise people experience at the sidewalk.

As an aside, I wonder about the degree to which changes to our cities are shaping the way we live. Take this chart, which shows how Americans have been meeting mates over the last 70 years.

Local networks – i.e. meeting people through neighbours or family – have steadily become less important, while friends and coworkers became more important before falling off a cliff over the last two decades. Online dating has risen up to supplant most other options – a sign of a time-poor society where opportunities for personal contact are increasingly limited?

In other areas, the adverse impacts of urban form are much more clear. Take Houston, for example. According to Tom Dart in the Guardian, one in five Houstonians are expected to be diabetic by 2040. This is a slow-motion public health disaster brought on by cheap sugar and car dependence:

Large homes sprout in the shadow of recently opened sections, promising cheap middle-class living with a heavy cost: a commute to central Houston of up to 90 minutes each way during rush hour, with minimal public transport options.

“A lot of time in Houston is spent in a car,” says Foreman, assistant director of Houston’s Department of Health and Human Services. This informs one of the Cities Changing Diabetes study’s most notable findings: that “time poverty” is among the risk factors in Houston for developing type 2 diabetes.

This means that young, relatively well-off people can also be considered a vulnerable population segment, even though they might not fit the traditional profile of people who may develop type 2 diabetes – that is, aged over 45, with high blood pressure and a high BMI, and perhaps disadvantaged through poverty or a lack of health insurance.

“You generally think of marginalised, lower income communities in poverty as your keys to health disparities but I think what we learned from our data in Houston is that we now have to expand the definition of what vulnerable is and what at-risk means. Just because we live in an urban environment, we may all indeed be vulnerable,” says Foreman.

In other words, not only its residents’ dietary choices but the way Houston is constructed as a city appears to be contributing to its diabetes problem, so tackling the issue requires architects as well as doctors; more sidewalks as well as fewer steaks.

People occasionally go on about how Auckland should be more like Houston. But the truth is that our public health system couldn’t afford it. As of 2013, 5.4% of NZ’s population was diagnosed with Type 2 diabetes. An earlier (2008) study found that our public health system spent $600 million annually treating people with diabetes. Imagine doubling or tripling that, as Houston is going to have to do.

While we’re talking about oil-rich theocracies, here’s an amusing BBC video on a Saudi Arabian sheikh’s sweet ride (WARNING: contains Jeremy Clarkson):

Also on the subject of gigantism, a Reddit user has helpfully compared several definitions of “high rise” buildings:

definition of high rise

Lastly, I’d like to highlight two important articles on the importance of politeness and kindness in debates.

First, Lindy West writes about her experience with internet trolling / online intimidation – in particular, “what happened when I confronted my cruellest troll“. Unfortunately, some people treat online anonymity as a license to bully and harass others, especially women who are speaking their minds. This is one of the reasons that Transportblog has strong user guidelines against disrespectful behaviour, ad hominem attacks, and bigotry:

For the past three years or so, at least one stranger has sought me out pretty much every day to call me a fat bitch (or some pithy variation thereof). I’m a writer and a woman and a feminist, and I write about big, fat, bitchy things that make people uncomfortable. And because I choose to do that as a career, I’m told, a constant barrage of abuse is just part of my job. Shrug. Nothing we can do. I’m asking for it, apparently.

Being harassed on the internet is such a normal, common part of my life that I’m always surprised when other people find it surprising. You’re telling me you don’t have hundreds of men popping into your cubicle in the accounting department of your mid-sized, regional dry-goods distributor to inform you that – hmm – you’re too fat to rape, but perhaps they’ll saw you up with an electric knife? No? Just me? People who don’t spend much time on the internet are invariably shocked to discover the barbarism – the eager abandonment of the social contract – that so many of us face simply for doing our jobs.

Others, of course, are willing to bully in person. When Auckland Council called a special session on its submissions to the independent Unitary Plan hearings panel on Wednesday, it invited along a range of people to speak. According to Hive News journalist Bernard Hickey, here’s what happened when youth group representatives got up to speak:

I watched this democratic deficit exposed most cruelly when the Council’s Youth Advisory Chair, Flora Apulu, spoke to the Council about how she felt the weight of the city’s half a million young people sitting on her shoulders as she argued for the affordable housing they desperately needed from this ‘up-zoned’ plan.

She was jeered and heckled by the dozens of rich, elderly and very Pakeha homeowners sitting just metres behind her. “Oh poor you,” they shouted.

Sudhvir Singh from Generation Zero was jeered even more loudly when he said the generation of home owners sitting behind him were ‘pulling up the ladder’ of home ownership on the young of today. “Poor you,” was the response again.

That’s it for the week. Go out and be kind to someone.

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47 comments

  1. Ooooohhhhh yes on the harrassment of women thing. I’ve collected a troll called Mark Baker on Facebook for daring to call out the NIMBYs. After he got tired of telling me how he owned 3 properties and I didn’t so I was a loser, he started throwing words like “unmedicated” around. I confess myself confused by a bully’s mindset. They must know that this kind of them makes THEM look bad rather than their target, right? But then the Gen-Zero submitters got almost as bad in person. It’s just a power thing – we can abuse you and you can’t do anything back.

      1. It’s something we consider when we’re in a mean mood, but ultimately it’s not our style to get personal. Also probably in violation of our own user guidelines!

    1. Primate dominance rituals, I guess. Puffing yourself up and baring your fangs works for chimpanzees, so why shouldn’t it work for humans? Kia kaha, Daphne!

  2. “This is one of the reasons that Transportblog has strong user guidelines against disrespectful behaviour, ad hominem attacks, and bigotry”

    …and it does remarkably well in that respect.

  3. Peter that mating chart is a great find. Discontinuity right there! Change is usually gradual; until it isn’t.

    What a clear image of the jump to a very different society, no wonder some older people are feeling bewildered and threatened by the world they suddenly find themselves in, all those old certainties just no longer relevant….

    1. Hard to believe 1-2% of people met online prior to mid 90‘s. In the 80‘s the only form of online I can remember is dial up bulleton boards. Not many people had computers, and most users would have been male. Pretty sure Internet Relay Chat only really started in the early 90‘s and only between universities.

      1. > Not many people had computers, and most users would have been male.

        Prior to the mid-1980s or so, computing was actually a fairly gender-mixed field. See e.g. http://www.npr.org/sections/money/2014/10/21/357629765/when-women-stopped-coding

        It also would have been more prestigious and exclusive, concentrated in academia and big business, so people would probably be more likely to admit it. That said, most of that “meeting online” would still count as having met through work, and 1-2% seems way too high. There wouldn’t have been 1% of people who were online at all.

    2. Except I would say that a change in the method of meeting someone isn’t “disruption” or “discontinuity” – the underlying social relationship (a couple) is unchanged. Too often we focus on the outward trapping of something and ignore the fact that the fundamental issue is constant and enduring.

      For example, with transport, I’d say the great changes were:
      1. The development of boats
      2. The development of the wheel
      3. The development of sealed (well, hard-facing) roads
      4. The development of the railway
      5, The development of the internal combustion engine (cars + planes)

      We talk about things like self-driving cars, Uber, being game changers, but really, they’re just different ways of doing the same thing; will they fundamentally affect society wherein people go from home to work for approximately 40 hours per week? Nope.

    1. Where there is demand for it, enabling more intensive development will allow land values to rise even as dwelling prices fall – the land owner can get more value out.

      Ironically, a solution that is *only* focused on lots and lots of greenfield land supply is more likely to put homeowners’ capital value at risk, as would tend to reduce land prices across the region without offering any opportunities to raise value by intensifying.

      1. And here we come to the crux of the matter: that additional value is only realised on sale.

        I am sure as an economist you can use the proper words, but the underlying issue for the NIMBYs is that currently they enjoy a level of utility from their properties (due to residing in them), a level that would be adversely affected by apartments next door; so their “residing value” (again there’s undoubtedly a better term) actually drops. It’s only their sale value that increaes.

        1. I would love to know how MHS buildings (no different in terms of bulk and setback from SHZ) actually affect their amenity. I really would.

  4. They have abandoned sense, they have abandoned manners – all we need now is religion “Jesus didn’t build apartments so neither should we” and Bingo – full blown Tea Party.

  5. Clearly the only logical solution to this unitary plan is to fill in the Orakei Basin and build new housing there. That way the Nimbys keep their precious low density and we don’t have all the expense of building on the fringes. God I wish I submitted that idea just to see the looks of horror on those grumpy old buggars faces!

    1. Well since it seems like the NIMBY’s may get an opportunity to resubmit you might still get your chance. I think it would make a great hoax story anyway. How about announce the Council is going to ressurrect plans from the ’70s to fill in Hobson Bay as a place to put the spoil from the CRL tunneling and then plant it in singe dwelling two storeyhousing. Just as much fun.

      1. I don’t know how they will get a chance to submit unless Council goes to Government to change the legislation. There is a timeline set by the legislation and the process moves on regardless. Council could ask for feedback, but that is not submissions and the feedback is not contestable through a hearing process. What does Council do with the feedback? What if 6 people like the re-zoning proposals for a street and 6 do not? What if Council does accept something from the consultation and wants to change something – do they then have to consult on that? Wher does it end and how long would it take?

  6. For anyone that is unsure as to how nice medium density 2/3/4/5 level apartments/townhouses can be take a look at Kensington Park – Orewa. That development is amazing. Sure it is at the higher end of the price scale (location, fitout, amenity etc) but something similar could be done in other parts of Auckland for a lot less.

      1. Images like these are a two-edged sword. I bet that examples like these of what you regard as good infill are exactly what press all the wrong buttons in those rich elderly pakehas who’ve spent their whole lives on leafy quarter acre blocks.

        I suspect that for people with ‘urbanist’ sympathies like most contributors to this blog it’s hard to fully grasp the depth of reactionary fear in the lifelong car-dependent suburbanite faced with the slightest change in the environment they’re used to.

  7. She was jeered and heckled by the dozens of rich, elderly and very Pakeha homeowners

    Or as in my copy of the Herald, “She was jeered and heckled by the dozens of elderly and predominantly Pakeha homeowners”

    WTF

  8. The moral to this story is very simple, if you don’t vote, the political system will shit on you.

    The sooner the young and poor wise up to this, the better things will be. Their participation rates are woeful.

  9. While the NIMBYs have won this particular battle, one gets the feeling this decision will actually go quite a long way towards losing them the war.

    Specifically, the IHP weighs submissions based on the quality of the evidence put forward. From my reading, submissions from organisations/people supporting intensification are more evidence-based than the submissions received from NIMBY groups. Council’s submission was intended to consider the relative merits of the both sides and find a reasonable compromise between them. Without Council’s submission, the IHP will now have to weigh the evidence themselves. And given the IHP isn’t worried about being re-elected, then it seems likely they will recommend greater upzoning than Council would have recommended.

    In this way, I think the NIMBYs have been strategically naieve. By forcing the Council to remove its submission, they have effectively created a vacuum into which the IHP can – based on the evidence contained in the submissions – recommend greater intensification. And such a recommendation would be consistent with the Unitary Plan, which arguably is more representative of Aucklanders views than a bunch of vocal yokels from the eastern suburbs.

    Finally, Wayne Walker’s comments indicate that he doesn’t understand some basic facts about housing markets. While upzoning can increase the value of land, it does so because it increases the number of dwellings that can be accommodated on that land. If the cost of land goes up by 100% but the number of dwellings increases by 150% than the cost of land per falls on a per dwelling basis. I find it quite scary that there is still confusion about these issues at such a late stage in the Unitary Plan process. The Councillors have had several years to understand these issues, and the fact Wayne Walker hasn’t would seem to indicate either 1) a lack of interest/commitment in relevant issues and/or 2) a lack of intellectual capacity. Both of which leave him ill-suited to the position of Councillor.

  10. You’re all quite funny. In your desire to bring down so called Nimbus you are hell bent on destroying what little is left that makes Auckland bearable which is nice leafy streets and properties that feel like homes. Turn it all into faceless concrete apartments built at the lowest price ( you would be very foolish indeed to think developers will do othrwise) and you will ultimately end up with ghetto accommodation and the associated social issues. It is your hated Nimbus who might actually be saving the little character that remains in Auckland. But hey you guys all know better. You are all experts.

    1. “Turn it all into faceless concrete apartments built at the lowest price ( you would be very foolish indeed to think developers will do othrwise)”

      Wrong. And I am speaking from direct experience.

    2. RB, while that is a totally legitimate concern, it actually is not necessary to construct faceless concrete apartments to increase density. It’s very common to have attractive three-story dwellings that still look like a villa and fit right in with the surrounding houses. Think of Melbourne, San Francisco, any Italian city, and they are lovely. How are we going to accommodate another million, another two million people in Auckland without everyone sharing the space they have a bit better?

      I think the answer to what you are saying is very tight controls on character and design for new housing, rather than trying to close the door to what I think is unavoidable population growth.

    3. The plan only involves 2 and 3 storey buildings in the areas the NIMBYs are hysterical about; the suggestion that this means anything other than highly finished desirable residences is either extraordinarily stupid or wilfully uncomprehending.

      In fact by pushing all urban growth to either distant farm land or lower value areas where the design build quality will be lower and transport and infrastructure costs way higher is the way to get instant slums added to Auckland’s already tatty housing stock.

      This debate is so full of nonsense it’s hard to keep up: We will only get improved dwelling stock by building better dwellings, and that can only happen where it is financially possible to do so, ie where there is demand and high enough value for it to be worth doing.

      For a city where apparently we are all obsessed with the property market are there really so many people with so little grasp of how such markets operate and within what constraints?

      1. Perhaps they believed all those stories about leaky town houses and apartment towers that their rates are paying to repair (with Council being “last man standing”)?

    4. I appreciate your concern for my wellbeing, but it’s not working out very well for me. I can’t afford a house anywhere within cooee of work, and there aren’t enough apartments being built to meet demand. Furthermore, the amenities that I enjoy – e.g. public parks, street trees, good restaurants – will hardly be destroyed by a few apartment buildings.

        1. I’m already saving more than 25% of my pre-tax income. If I changed to a diet of lentils and rice I could add a few percentage points to that. It wouldn’t fundamentally change the fact that home prices have risen faster than I can save.

          1. Same here saving over 30% of gross income but can’t save enough to keep up with capital gains on a 20% deposit in Auckland and I have a high paying graduate engineering role

          2. Sorry, but we have absolutely no right to do this to our young people

            The combination of the Council preventing low-cost housing coming into the market, and the Government giving speculators a helping hand on purchasing what little does become available, is making it impossible for this generation get ahead.

            It’s terrible that in a time of housing shortage the Government is still handing out tax incentives to investors so that they can take two, three or more houses in Auckland. It seems to me that this could easily be reversed in favour of first-home buyers with a paragraph in the next budget, Then we could at least concentrate on how to get new builds going in the knowledge that they will be available to meet the need of new home buyers before the greed of investors.

  11. As an economist, I cannot disagree strongly enough with this bizarre analysis.

    Wayne Walker’s base assumption is stuffed, no amount of upzoning is going to increase value in Auckland. Development in Auckland is currently unaffordable, our median land cost is higher than Sydney and twice as high as Brisbane. We have a higher property price and slower rate of development, because costs are already too high.

  12. It’s totally predictable that at a town hall meeting the angriest people will hog the attention. Town hall meetings may be a nice symbol of grassroots democracy, but they are obviously useless as a way of gauging public opinion as a whole because of the selection bias of the people involved.

    If a government authority really wants to gauge public opinion on an issue (as opposed to just putting on a show to let people feel involved) it HAS to do a statistically valid sample survey of the whole population. Have they done so as part of this process?

  13. But it’s fair to say that the workings of housing markets are extremely complex and often counterintuitive.

    Melbourne and Brisbane make vast tracts of land available for sprawling suburban expansion. This has resulted in an apartment building boom – with multi-unit dwellings being planned at a rates 4 times quicker than single dwelling houses.

    http://www.smh.com.au/business/property/brisbane-unit-approvals-skyrocket-20150716-gie6b9.html
    http://www.afr.com/real-estate/melbourne-brisbane-apartments-tipped-for-rising-vacancy-and-reduced-rents-20151215-glnqel

    1. You know that Melbourne and Sydney both have urban growth boundaries, right?

      I was over in Sydney last week for work. From what I can see in the plans and on the ground, a key enabler in their current apartment boom is the willingness of councils to rezone brownfield industrial sites and public housing estates for dramatically higher density – i.e. 8-16 storey apartment buildings, rather than the tentative move towards 3-7 storeys we’re seeing in Auckland. Height limits matter!

      1. Sydney has a more restrictive growth boundary and much higher land prices than Melbourne. Sydney has the second highest median land price of the Australasian markets. Sydney is therefore adding dwellings much slower than Melbourne and likely to have a housing shortfall persisting through to the mid-2020s. Melbourne is likely to move into surplus next year. Of course neither is as bad as Auckland, where the land price is highest and we are expecting a housing shortfall to persist until the late-2030s.

        Brownfield sites on converted quarries or golf courses or old public housing are great, because they are land which is pre-accumulated – meaning they have a lower cost. Also owners (councils particularly) are sometimes willing to sell at a lower than market rate. These sites represent a great profit for any developer able to secure the rights to build. However they aren’t the quickest way for developing a city.

      2. Rezoning Penrose for 16 storey apartments would work. Fletchers were in favour of this as one of the largest land owners in that area.

        1. They better do it soon, if it splits away the property division will want to sell at full price and the construction division will no longer be able to get the land cheap.

  14. I watched Wayne on the live stream. Can you imagine my personal pride in having him as my Councillor when he said all that. The twits who set up the supercity lumped us in with Orewa despite the fact I live close to Kingsland than Orewa! Any ever since the people of Orewa have used their votes to prevent able people like Margaret Miles or Julia Parfitt getting on to the Council to represent us. Supercity? Over $1billion on a crap IT system and councillors who are not as good as the ones we had before.

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