Originally published May 2022.

When I first moved to London 20 years ago, the sight of a parakeet was a relatively rare occurrence, a pleasant surprise. I would only see them when I visited certain parts of town, such as Richmond Park. It remained that way for many years.

Then, a few years ago, they suddenly seemed to be everywhere. Today, they are a daily sight in my neighbourhood and many others. Indeed, the most recent estimate I have seen suggests there are 30,000 ring-necked parakeets in the capital.

What happened? I have found myself asking whether it’s a result of warmer winters, fewer predators, new food sources or more green spaces?

There must be some explanation, right?

Wrong.

While there have been sightings of parakeets in London since Victorian times, it’s thought that they didn’t start breeding in the wild until the late 1960s.

Let’s simplistically assume that parakeets die, find mates and raise chicks such that the population grows by 20% per year. Holding that rate of growth constant, two breeding pairs in 1969 could lead to a population of 30,000 by 2018.

Such a growth rate would have meant that there were less than 2,000 parakeets in London 20 years ago. But the compounding effect means that each year the growth in the absolute numbers gets larger. The population could have increased by around 20,000 between 2012 and 2018 without any change in the rate of growth.

“Looking for an explanation as to why I was suddenly seeing parakeets more regularly, I had fallen into the trap of always expecting to see linear growth“

So, it’s quite possible that there was no disjuncture, no change in the propensity of the population to grow. It just felt that way. In looking for an explanation as to why I was suddenly seeing parakeets more regularly, I had fallen into the trap of always expecting to see linear growth.

My brain wants to make simple straight lines, but often life is not like that.

‘Linear Thinking in a Nonlinear World’, published by the Harvard Business Review, is an excellent article that illustrates numerous traps our brains set for us by wanting to make simple straight lines. “Decades of research in cognitive psychology show that the human mind struggles to understand nonlinear relationships,” the authors state.

They provide some great examples of how non-linear thinking can be counterintuitive.

For example, “It will surprise most drivers that going from 40 to 65 will save you about six minutes per 10 miles, but going from 65 to 90 saves only about two and a half minutes, even though you’re increasing your speed 25 miles per hour in both instances.”

The article offers a real estate example: residential mortgages.

In the early years of a loan, property owners are often disappointed at how gradually they reduce their debt. If they sell, they can be surprised by how meagre their net gains are. But if they hold on to the property, they may be pleasantly surprised by how quickly it drops in later years.

The key point is that the principal doesn’t decrease linearly. And wherever relationships are non-linear, they can be hard to grasp.

This applies to our thinking about cities too. Cites are networks and power laws apply. Both policymakers and property investors need to understand this.

“Co-location makes the exchange of goods and ideas easier and cheaper”

Generally, the more companies locate in a city, the more productive they are. This is due to agglomeration economies, which Ed Glaser has defined as “the benefits that come when firms and people locate near one another together in cities and industrial clusters.” Co-location makes the exchange of goods and ideas easier and cheaper. It can make labour markets work more efficiently too.

That this is true is intuitive. Being close together means the costs of meeting suppliers, partners and customers are lower. You’re more likely to bump into people and find out what the competition is up to. More knowledge is shared, more ideas are generated, teams create, firms innovate and become more productive.

What may not be intuitive is the extent to which this is true.

In his fascinating book, Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies, Geoffrey West highlights the clear relationship between city size and proxies for productivity.

West shows that, as with other socioeconomic characteristics, metrics such as GDP, wages and patents scale in a surprisingly regular and systematic manner. For any country, if you know the size of the city, you can predict how productive people will be with a good degree of accuracy. Crucially, these metrics scale in a super-linear fashion – with an exponent of around 1.15.

Our tendency to think linearly leaves us poorly equipped to intuit how marked the differences can be between towns and cities of different sizes.

Consider the difference between the productivity of a worker in a small town of say 30,000 people and a worker in Birmingham with a population of around a million. Applying an exponent of 1.15 suggests the worker in Birmingham would not be a little bit more productive, but twice as productive. Furthermore, a worker in London could be an extra 50% more productive than the Birmingham worker.

So scale matters. Perhaps more than you think. Agglomeration benefits tend to increase at an exponential rate as cities increase in size. Larger cities are more productive simply because they are larger. Much more productive, in fact.

For policymakers, this implies that if a counterbalance to London is desirable, investment needs to be focused on a few of the UK’s other largest cities (and reducing barriers to accessing their labour markets).

Meanwhile, it helps real estate investors to know that the returns to physical proximity are high for knowledge-intensive activities. Financial services or technology firms are willing and able to pay substantially higher rents to locate at the heart of large cities.

Could an increase in remote working challenge this? We don’t know. But owners of well-located real estate in major cities can take comfort from the fact that in the past communication technology has acted as a complement to rather than a substitute for face-to-face interaction.

So, if history is a guide, the greater capacity for remote work could result in workplaces being more intensively used to leverage the benefits of physical proximity.

Workplaces need to be spaces that people choose to spend their time, that succeed in bringing people to collaborate, build trust and develop relationships.

Succeed in doing that and we may continue to be surprised by the scale of advantage larger cities enjoy.