Before concluding this unit, I'd like to offer some thoughts
and reflections and opinions on urban scaling.
Sort of take stock, kind of give you a sense of things, at least my opinion of them.
So first, studying properties of cities is an important and really difficult issue.
They're definitely complex systems.
They're made up of a large number of strongly interacting entities,
and those entities are often
heterogeneous. They're not all the same.
And entities, here, I'm thinking not only of people, of course,
but also the networks and infrastructure, social and physical,
that support those people.
So they're definitely complex systems, and they're important because
I think the majority of us live in cities,
and all indications are that the world population
will become more and more urbanized in the years ahead.
And cities give us good things, like income, health, creativity, new ideas,
but they can also bring bad things:
disease and crime, pollution and climate change,
and so understanding their properties is important,
and just on a personal note, maybe having grown up in a big city,
I find cities fascinating to think about. I enjoy traversing through cities
(even though I live in a small town now)
and thinking about all the different things that makes up a city.
So, some thoughts on this work:
First, um, data in some level, or reliable data,
is perhaps hard to come by.
It's very different than, say, studying a physical system
where it's easier --- relatively easy ---
to measure properties, and properties are static, and so on.
So, some of the things that I have in mind when thinking about
economic outputs of cities, I suppose that could be measured by taxes
and revenue and so on,
but an awful lot of economic activity goes on in an informal...
it's in the informal sector
that never gets measured or captured by any official...
any official metric.
So people might exchange services and goods without going through any sort of
official entity, and so those transactions might not get recorded
and entered into this record, but surely they're an important part
of the fabric of urban life.
Additionally, there are a lot of people who, for one reason or another,
are undocumented, and may be uncounted in these estimates of population.
Here in the U.S., we have a large population that we refer to as 'undocumented'
or sometimes, unfortunately, as 'illegal', and as I'm recording this,
the European... the migrant crisis in Europe is a huge issue.
Thousands and thousands and thousands of displaced people,
and with continued civil war and continued climate change,
we're witnessing more and more migration of refugees across the world,
and those people aren't always counted.
So, um, sometimes an estimate of
a city population, it looks like a good hard number because
it's there in black and white on a piece of paper, but it's hard to know how many people
actually live in cities.
So, anyway, these are some things I think about as I look at this data.
Additionally, um, the data itself is messy,
which is not surprising because the world is messy and cities are a little bit messy,
and by 'messy', I mean, if we plot the data on our favorite way, a log-log plot,
we definitely see a trend (this thing here on the left)
There's definitely a clear trend,
but there's a lot of variation around that trend as well. So we can
certainly fit a trend line and that's a
reasonable thing to do. But is this exactly
a power law? Well... surely not. Right? Because there's an awful lot of spread
around this. Is it even best described by
a power law? Maybe a log-normal is a better... um... functional form to assume
for this. And I think there's some evidence to suggest that actually
log-normals may be better. Or that it's difficult to state with confidence
that these really are power laws.
So there's some question about data analysis as well.
On the other hand, one of the themes of this course is that fractal is not
necessarily a yes/no quantity. Things are more or less fractal-like
if they exhibit approximate scaling to a lesser or greater degree.
So I think that it's certainly a reasonable
thing to do to fit a power law to this and then to sort of draw
inferences from that. But there's some
questions about the data analysis for this
Is it really a power law, is that the best way
to think about this? I tend to think it's
an OK way to think about it... but it's an
area of some controversy, and there's certainly
not universal agreement. So, regardless, there certainly is some trend
here and you can describe this trend with
various exponents. And that, at this
point is just an empirical relationship.
We notice that there is some pattern between, say, population and
road length. Or population and economic
output, measured one of any of a number of different ways.
So that observation, that empirical observation
in and of itself, I think is interesting intrinsically,
and is certainly useful as well. Because
it lets us make certain predictions, on average, about what might happen
as cities get larger. What sort of resources
will they use, what sort of benefits might
we see from those cities, what sort of
drawbacks might we see from those cities?
So, saying a relationship is only empirical
doesn't necessarily mean that it's not
a useful or interesting relationship. So
then the question is, though, can we
say more than, "Gee, this is an empirical
relationship"? Can we speak to the potential
mechanisms that would generate these
sorts of scaling behaviours, that are seen
more or less. And here I think that this is
very much work that is ongoing. Initial efforts seem to me to be promising
but at least in my opinion, I don't think
it's sort of, the final word. There's not
a solidified theory the way there is for
metabolic scaling in the West-Brown-Lindquist theory.
It takes time to develop ideas, to sift
through what the important assumptions are
what the not important assumptions are, and
that process is ongoing. Additionally,
one thing that is maybe left out of this
analysis, and I think it's just worth
mentioning but not dwelling on,
is the idea of intentionality. That
cities, and particularly the people who
inhabit them, can exhibit choice,
intention, design, in how they build
cities. So there are clearly some constraints
almost metabolic constraints, in terms of
power lines and water mains and roads
and paths and so on. But there's also room for
for choices. I think that's worth keeping in mind
as well, that we're studying cities,
perhaps as if they were organisms, in
analogy with metabolic systems, and that
analogy is a powerful one, a very productive
one, but it's probably not the only way to talk about cities, and it's useful
to remember - at least I hope - that we have some choice in how cities develop
It's not necessarily inevitable. In any event, I don't mean any of these
comments to be overly critical, or at all negative towards urban scaling theory.
I think it's a really fascinating area. It's provocative, gets me to think
about cities in interesting ways, and I
think already has produced some
useful results, these empirical regularities. Recognition, that is
that there are these empirical regularities
in how certain properties of cities scale
So, again, this is an ongoing area of
research. I'm excited to see how it
develops over the next few years, or decades, and I hope that
this introduction has been useful for you
and that you can follow along and
maybe contribute to this effort as well.